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La ecuación:
Ecuación x^2+3x=4
Ecuación (11x+14)-(5x-8)=25
Ecuación 11/(x-9)=-10
Ecuación z^4+16=0
Expresar {x} en función de y en la ecuación:
-18*x+8*y=-2
-11*x-14*y=-3
12*x+12*y=-14
-2*x+20*y=-2
Integral de d{x}:
1/cosx
Derivada de:
1/cosx
Gráfico de la función y =:
1/cosx
Expresiones idénticas
y^ dos +y*tgx= uno /cosx
y al cuadrado más y multiplicar por tgx es igual a 1 dividir por coseno de x
y en el grado dos más y multiplicar por tgx es igual a uno dividir por coseno de x
y2+y*tgx=1/cosx
y²+y*tgx=1/cosx
y en el grado 2+y*tgx=1/cosx
y^2+ytgx=1/cosx
y2+ytgx=1/cosx
y^2+y*tgx=1 dividir por cosx
Expresiones semejantes
y-1/cos(x)=0
(cos(x)-1)/cos(x)+2*sin(x)*cot(x)=0
(1/cos(x)^2)=0
y^2-y*tgx=1/cosx
Expresiones con funciones
tgx
tgx=-(3/4)
tgx=5/3
tgx-x=5
tgx+sqrt3=0
tgx/2-✓3=0
cosx
cosx=−0,9:
cosx=c+2
cosx/2=sinи
cosx+sinx=-0,5
cosx/3=sqrt(x-1)

y^2+y*tgx=1/cosx la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 2                1   
y  + y*tan(x) = ------
                cos(x)

y^{2} + y \tan{\left(x \right)} = \frac{1}{\cos{\left(x \right)}}

Simplificar

Solución detallada

Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.

La ecuación se convierte de

y^{2} + y \tan{\left(x \right)} = \frac{1}{\cos{\left(x \right)}}

\left(y^{2} + y \tan{\left(x \right)}\right) - \frac{1}{\cos{\left(x \right)}} = 0

Es la ecuación de la forma

a*y^2 + b*y + c = 0

La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:

y_{1} = \frac{\sqrt{D} - b}{2 a}

y_{2} = \frac{- \sqrt{D} - b}{2 a}

donde D = b^2 - 4*a*c es el discriminante.
Como

a = 1

b = \tan{\left(x \right)}

c = - \frac{1}{\cos{\left(x \right)}}

, entonces

D = b^2 - 4 * a * c =

(tan(x))^2 - 4 * (1) * (-1/cos(x)) = tan(x)^2 + 4/cos(x)

La ecuación tiene dos raíces.

y1 = (-b + sqrt(D)) / (2*a)

y2 = (-b - sqrt(D)) / (2*a)

y_{1} = \frac{\sqrt{\tan^{2}{\left(x \right)} + \frac{4}{\cos{\left(x \right)}}}}{2} - \frac{\tan{\left(x \right)}}{2}

y_{2} = - \frac{\sqrt{\tan^{2}{\left(x \right)} + \frac{4}{\cos{\left(x \right)}}}}{2} - \frac{\tan{\left(x \right)}}{2}

Teorema de Cardano-Vieta

es ecuación cuadrática reducida

p y + q + y^{2} = 0

donde

p = \frac{b}{a}

p = \tan{\left(x \right)}

q = \frac{c}{a}

q = - \frac{1}{\cos{\left(x \right)}}

Fórmulas de Cardano-Vieta

y_{1} + y_{2} = - p

y_{1} y_{2} = q

y_{1} + y_{2} = - \tan{\left(x \right)}

y_{1} y_{2} = - \frac{1}{\cos{\left(x \right)}}

Gráfica

Respuesta rápida [src]

       //    ____________________________________________________________________________________________________________________________________________________________________                                                                                                                                                                                                 \                          /    ____________________________________________________________________________________________________________________________________________________________________                                                                                                                                                                                                 \                       \   /    ____________________________________________________________________________________________________________________________________________________________________                                                                                                                                                                                                 \                          /    ____________________________________________________________________________________________________________________________________________________________________                                                                                                                                                                                                 \                       
       ||   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                          |   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                       |   |   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                          |   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                       
       ||4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                       |   |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                       
       ||\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cosh(im(x))*sin(re(x))|*sin(re(x))*sinh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x))|   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cosh(im(x))*sin(re(x))|*cos(re(x))*cosh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))
       |\                                                                                                                                                                            \                                                                                2                                                                                 /                         /                          \                                                                                                                                                                            \                                                                                2                                                                                 /                         /                       |   \                                                                                                                                                                            \                                                                                2                                                                                 /                         /                          \                                                                                                                                                                            \                                                                                2                                                                                 /                         /                       
y1 = I*|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
       |                                                                                                                                                                       /   2            2             2            2       \                                                                                                                                                                                                                                                                                                                                                /   2            2             2            2       \                                                                                                                                                                      |                                                                                                                                                                          /   2            2             2            2       \                                                                                                                                                                                                                                                                                                                                                /   2            2             2            2       \                                                                                                                                                                      
       \                                                                                                                                                                     2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                      /                                                                                                                                                                        2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/

y_{1} = - \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + i \left(\frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)}\right)

       /  /    ____________________________________________________________________________________________________________________________________________________________________                                                                                                                                                                                                 \                          /    ____________________________________________________________________________________________________________________________________________________________________                                                                                                                                                                                                 \                       \   /    ____________________________________________________________________________________________________________________________________________________________________                                                                                                                                                                                                 \                          /    ____________________________________________________________________________________________________________________________________________________________________                                                                                                                                                                                                 \                       
       |  |   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                          |   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                       |   |   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                          |   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                       
       |  |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                       |   |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                       
       |  |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cosh(im(x))*sin(re(x))|*sin(re(x))*sinh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x))|   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cosh(im(x))*sin(re(x))|*cos(re(x))*cosh(im(x))
       |  \                                                                                                                                                                            \                                                                                2                                                                                 /                         /                          \                                                                                                                                                                            \                                                                                2                                                                                 /                         /                       |   \                                                                                                                                                                            \                                                                                2                                                                                 /                         /                          \                                                                                                                                                                            \                                                                                2                                                                                 /                         /                       
y2 = I*|- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
       |                                                                                                                                                                         /   2            2             2            2       \                                                                                                                                                                                                                                                                                                                                                /   2            2             2            2       \                                                                                                                                                                      |                                                                                                                                                                          /   2            2             2            2       \                                                                                                                                                                                                                                                                                                                                                /   2            2             2            2       \                                                                                                                                                                      
       \                                                                                                                                                                       2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                      /                                                                                                                                                                        2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/

y_{2} = \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} - \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + i \left(- \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} - \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)}\right)

y2 = (((2*sin(re(x))*cos(re(x))*sinh(im(x))*cosh(im(x)) - 4*sin(re(x))*sinh(im(x)))^2 + (sin(re(x))^2*cosh(im(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 4*cos(re(x))*cosh(im(x)))^2)^(1/4)*sin(atan2(2*sin(re(x))*cos(re(x))*sinh(im(x))*cosh(im(x)) - 4*sin(re(x))*sinh(im(x), sin(re(x))^2*cosh(im(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 4*cos(re(x))*cosh(im(x)))/2) + cos(re(x))*sinh(im(x)))*sin(re(x))*sinh(im(x))/(2*(sin(re(x))^2*sinh(im(x))^2 + cos(re(x))^2*cosh(im(x))^2)) - (((2*sin(re(x))*cos(re(x))*sinh(im(x))*cosh(im(x)) - 4*sin(re(x))*sinh(im(x)))^2 + (sin(re(x))^2*cosh(im(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 4*cos(re(x))*cosh(im(x)))^2)^(1/4)*cos(atan2(2*sin(re(x))*cos(re(x))*sinh(im(x))*cosh(im(x)) - 4*sin(re(x))*sinh(im(x)), sin(re(x))^2*cosh(im(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 4*cos(re(x))*cosh(im(x)))/2) + sin(re(x))*cosh(im(x)))*cos(re(x))*cosh(im(x))/(2*(sin(re(x))^2*sinh(im(x))^2 + cos(re(x))^2*cosh(im(x))^2)) + i*(-(((2*sin(re(x))*cos(re(x))*sinh(im(x))*cosh(im(x)) - 4*sin(re(x))*sinh(im(x)))^2 + (sin(re(x))^2*cosh(im(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 4*cos(re(x))*cosh(im(x)))^2)^(1/4)*sin(atan2(2*sin(re(x))*cos(re(x))*sinh(im(x))*cosh(im(x)) - 4*sin(re(x))*sinh(im(x)), sin(re(x))^2*cosh(im(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 4*cos(re(x))*cosh(im(x)))/2) + cos(re(x))*sinh(im(x)))*cos(re(x))*cosh(im(x))/(2*(sin(re(x))^2*sinh(im(x))^2 + cos(re(x))^2*cosh(im(x))^2)) - (((2*sin(re(x))*cos(re(x))*sinh(im(x))*cosh(im(x)) - 4*sin(re(x))*sinh(im(x)))^2 + (sin(re(x))^2*cosh(im(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 4*cos(re(x))*cosh(im(x)))^2)^(1/4)*cos(atan2(2*sin(re(x))*cos(re(x))*sinh(im(x))*cosh(im(x)) - 4*sin(re(x))*sinh(im(x)), sin(re(x))^2*cosh(im(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 4*cos(re(x))*cosh(im(x)))/2) + sin(re(x))*cosh(im(x)))*sin(re(x))*sinh(im(x))/(2*(sin(re(x))^2*sinh(im(x))^2 + cos(re(x))^2*cosh(im(x))^2))))

Suma y producto de raíces [src]

suma

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  ||4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                       |   |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                            |  |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                       |   |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                       
  ||\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cosh(im(x))*sin(re(x))|*sin(re(x))*sinh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x))|   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cosh(im(x))*sin(re(x))|*cos(re(x))*cosh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))     |  |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cosh(im(x))*sin(re(x))|*sin(re(x))*sinh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x))|   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cosh(im(x))*sin(re(x))|*cos(re(x))*cosh(im(x))
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I*|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + I*|- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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  \                                                                                                                                                                     2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                      /                                                                                                                                                                        2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                           \                                                                                                                                                                       2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                      /                                                                                                                                                                        2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/

\left(- \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + i \left(\frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)}\right)\right) + \left(\frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} - \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + i \left(- \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} - \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)}\right)\right)

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  ||4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                       |     |  |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                       |   |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                       
  ||\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cosh(im(x))*sin(re(x))|*sin(re(x))*sinh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x))|     |  |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cosh(im(x))*sin(re(x))|*sin(re(x))*sinh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x))|   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cosh(im(x))*sin(re(x))|*cos(re(x))*cosh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cosh(im(x))*sin(re(x))|*cos(re(x))*cosh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))
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I*|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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  \                                                                                                                                                                     2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                      /     \                                                                                                                                                                       2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                      /                                                                                                                                                                        2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/

- \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} - \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + i \left(\frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)}\right) + i \left(- \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} - \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)}\right)

producto

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|  ||   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                          |   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                       |   |   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                          |   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                       | |  |  |   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                          |   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                       |   |   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                          |   /                                                                                                                                                                  2     /     /                                                                                 2           2             2            2                                  \\                         |                       |
|  ||4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                       |   |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                       | |  |  |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                       |   |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                          |4 /                                                                               2   /    2           2             2            2                                  \      |atan2\-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                         |                       |
|  ||\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cosh(im(x))*sin(re(x))|*sin(re(x))*sinh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x))|   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cosh(im(x))*sin(re(x))|*cos(re(x))*cosh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| - cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))| |  |  |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cosh(im(x))*sin(re(x))|*sin(re(x))*sinh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x))|   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))   |\/   (-4*sin(re(x))*sinh(im(x)) + 2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)))  + \cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/  *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| + cosh(im(x))*sin(re(x))|*cos(re(x))*cosh(im(x))|
|  |\                                                                                                                                                                            \                                                                                2                                                                                 /                         /                          \                                                                                                                                                                            \                                                                                2                                                                                 /                         /                       |   \                                                                                                                                                                            \                                                                                2                                                                                 /                         /                          \                                                                                                                                                                            \                                                                                2                                                                                 /                         /                       | |  |  \                                                                                                                                                                            \                                                                                2                                                                                 /                         /                          \                                                                                                                                                                            \                                                                                2                                                                                 /                         /                       |   \                                                                                                                                                                            \                                                                                2                                                                                 /                         /                          \                                                                                                                                                                            \                                                                                2                                                                                 /                         /                       |
|I*|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|I*|- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
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\  \                                                                                                                                                                     2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                      /                                                                                                                                                                        2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                      / \  \                                                                                                                                                                       2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                      /                                                                                                                                                                        2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                                                                                                                                                                                              2*\cos (re(x))*cosh (im(x)) + sin (re(x))*sinh (im(x))/                                                                                                                                                                      /

\left(- \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + i \left(\frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} - \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)}\right)\right) \left(\frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} - \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} + i \left(- \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)} - \frac{\left(\sqrt[4]{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2} + \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 4 \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}\right)}\right)\right)

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________     /     /                                                            2           2             2            2                                  \\                                  __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________     /     /                                                            2           2             2            2                                  \\                            
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              /         2                2                              2    4                              2    4               3                             2           2               4                             3                            2                              2                             2                                                         2    2           2               2           2                              2                                   2|atan2\2*(-2 + cos(re(x))*cosh(im(x)))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                                 /         2                2                              2    4                              2    4               3                             2           2               4                             3                            2                              2                             2                                                         2    2           2               2           2                              2                                   2|atan2\2*(-2 + cos(re(x))*cosh(im(x)))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|                            
   2             2            /                                         __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________    /     /                                                            2           2             2            2                                  \\    /     /                                                            2           2             2            2                                  \\\   \/  - 32*sin (re(x)) + 32*cos (re(x)) + (-1 + cosh(2*im(x))) *cos (re(x)) + (-1 + cosh(2*im(x))) *sin (re(x)) - 8*cos (re(x))*cosh(3*im(x)) - 4*cos (re(x))*sin (re(x)) + 4*sin (re(x))*cosh(2*im(x)) + 8*cos (re(x))*cosh(im(x)) + 32*cos (re(x))*cosh(2*im(x)) + 32*sin (re(x))*cosh(2*im(x)) - 8*sin (re(x))*cos(re(x))*cosh(3*im(x)) + 2*(-1 + cosh(2*im(x))) *cos (re(x))*sin (re(x)) + 4*cos (re(x))*sin (re(x))*cosh(2*im(x)) + 40*sin (re(x))*cos(re(x))*cosh(im(x)) *sin |---------------------------------------------------------------------------------------------------------------------------------------------|      2                        \/  - 32*sin (re(x)) + 32*cos (re(x)) + (-1 + cosh(2*im(x))) *cos (re(x)) + (-1 + cosh(2*im(x))) *sin (re(x)) - 8*cos (re(x))*cosh(3*im(x)) - 4*cos (re(x))*sin (re(x)) + 4*sin (re(x))*cosh(2*im(x)) + 8*cos (re(x))*cosh(im(x)) + 32*cos (re(x))*cosh(2*im(x)) + 32*sin (re(x))*cosh(2*im(x)) - 8*sin (re(x))*cos(re(x))*cosh(3*im(x)) + 2*(-1 + cosh(2*im(x))) *cos (re(x))*sin (re(x)) + 4*cos (re(x))*sin (re(x))*cosh(2*im(x)) + 40*sin (re(x))*cos(re(x))*cosh(im(x)) *cos |---------------------------------------------------------------------------------------------------------------------------------------------|      2                     
cos (re(x))   sin (re(x))     |                                        /         2                2                              2    4                              2    4               3                             2           2               4                             3                            2                              2                             2                                                         2    2           2               2           2                              2                                   |atan2\2*(-2 + cos(re(x))*cosh(im(x)))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/|    |atan2\2*(-2 + cos(re(x))*cosh(im(x)))*sin(re(x))*sinh(im(x)), cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x)) + 4*cos(re(x))*cosh(im(x))/||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     \                                                                      2                                                                      /   sin (re(x))*cosh(2*im(x))                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     \                                                                      2                                                                      /   cos (re(x))*cosh(2*im(x))
----------- + ----------- + I*|cos(re(x))*sin(re(x))*sinh(2*im(x)) - \/  - 32*sin (re(x)) + 32*cos (re(x)) + (-1 + cosh(2*im(x))) *cos (re(x)) + (-1 + cosh(2*im(x))) *sin (re(x)) - 8*cos (re(x))*cosh(3*im(x)) - 4*cos (re(x))*sin (re(x)) + 4*sin (re(x))*cosh(2*im(x)) + 8*cos (re(x))*cosh(im(x)) + 32*cos (re(x))*cosh(2*im(x)) + 32*sin (re(x))*cosh(2*im(x)) - 8*sin (re(x))*cos(re(x))*cosh(3*im(x)) + 2*(-1 + cosh(2*im(x))) *cos (re(x))*sin (re(x)) + 4*cos (re(x))*sin (re(x))*cosh(2*im(x)) + 40*sin (re(x))*cos(re(x))*cosh(im(x)) *cos|---------------------------------------------------------------------------------------------------------------------------------------------|*sin|---------------------------------------------------------------------------------------------------------------------------------------------|| + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------
     2             2          \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       \                                                                      2                                                                      /    \                                                                      2                                                                      //                                                                                                                                                                                                                                                                                                                   2                                                                                                                                                                                                                                                                                                                               2                                                                                                                                                                                                                                                                                                                               2                                                                                                                                                                                                                                                                                                                               2            
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 4*(-cos(re(x))*cosh(im(x)) + I*sin(re(x))*sinh(im(x)))

\frac{i \left(- \sqrt{\left(\cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 1\right)^{2} \sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} + 2 \left(\cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 1\right)^{2} \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} + \left(\cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 1\right)^{2} \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} + 4 \sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} + 40 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 8 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(3 \operatorname{im}{\left(x\right)} \right)} + 32 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 32 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} + 8 \cos^{3}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 8 \cos^{3}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(3 \operatorname{im}{\left(x\right)} \right)} + 32 \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} + 32 \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \left(\cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 2\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \left(\cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 2\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)} + \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(x\right)} \right)}\right) + \frac{\sqrt{\left(\cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 1\right)^{2} \sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} + 2 \left(\cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 1\right)^{2} \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} + \left(\cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 1\right)^{2} \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} + 4 \sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} + 40 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 8 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(3 \operatorname{im}{\left(x\right)} \right)} + 32 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 32 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} + 8 \cos^{3}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 8 \cos^{3}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(3 \operatorname{im}{\left(x\right)} \right)} + 32 \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} + 32 \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(2 \left(\cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 2\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)}}{2} - \frac{\sqrt{\left(\cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 1\right)^{2} \sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} + 2 \left(\cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 1\right)^{2} \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} + \left(\cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 1\right)^{2} \cos^{4}{\left(\operatorname{re}{\left(x\right)} \right)} + 4 \sin^{4}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} + 40 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 8 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(3 \operatorname{im}{\left(x\right)} \right)} + 32 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} - 32 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} + 8 \cos^{3}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 8 \cos^{3}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(3 \operatorname{im}{\left(x\right)} \right)} + 32 \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)} + 32 \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)}} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(2 \left(\cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} - 2\right) \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)},\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} - \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} + 4 \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)} \right)}}{2} \right)}}{2} + \frac{\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)}}{2} + \frac{\sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)}}{2} - \frac{\cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(x\right)} \right)}}{2} + \frac{\cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)}}{2}}{4 \left(i \sin{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)} - \cos{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)^{2}}

(cos(re(x))^2/2 + sin(re(x))^2/2 + i*(cos(re(x))*sin(re(x))*sinh(2*im(x)) - sqrt(-32*sin(re(x))^2 + 32*cos(re(x))^2 + (-1 + cosh(2*im(x)))^2*cos(re(x))^4 + (-1 + cosh(2*im(x)))^2*sin(re(x))^4 - 8*cos(re(x))^3*cosh(3*im(x)) - 4*cos(re(x))^2*sin(re(x))^2 + 4*sin(re(x))^4*cosh(2*im(x)) + 8*cos(re(x))^3*cosh(im(x)) + 32*cos(re(x))^2*cosh(2*im(x)) + 32*sin(re(x))^2*cosh(2*im(x)) - 8*sin(re(x))^2*cos(re(x))*cosh(3*im(x)) + 2*(-1 + cosh(2*im(x)))^2*cos(re(x))^2*sin(re(x))^2 + 4*cos(re(x))^2*sin(re(x))^2*cosh(2*im(x)) + 40*sin(re(x))^2*cos(re(x))*cosh(im(x)))*cos(atan2(2*(-2 + cos(re(x))*cosh(im(x)))*sin(re(x))*sinh(im(x)), cosh(im(x))^2*sin(re(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 4*cos(re(x))*cosh(im(x)))/2)*sin(atan2(2*(-2 + cos(re(x))*cosh(im(x)))*sin(re(x))*sinh(im(x)), cosh(im(x))^2*sin(re(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 4*cos(re(x))*cosh(im(x)))/2)) + sqrt(-32*sin(re(x))^2 + 32*cos(re(x))^2 + (-1 + cosh(2*im(x)))^2*cos(re(x))^4 + (-1 + cosh(2*im(x)))^2*sin(re(x))^4 - 8*cos(re(x))^3*cosh(3*im(x)) - 4*cos(re(x))^2*sin(re(x))^2 + 4*sin(re(x))^4*cosh(2*im(x)) + 8*cos(re(x))^3*cosh(im(x)) + 32*cos(re(x))^2*cosh(2*im(x)) + 32*sin(re(x))^2*cosh(2*im(x)) - 8*sin(re(x))^2*cos(re(x))*cosh(3*im(x)) + 2*(-1 + cosh(2*im(x)))^2*cos(re(x))^2*sin(re(x))^2 + 4*cos(re(x))^2*sin(re(x))^2*cosh(2*im(x)) + 40*sin(re(x))^2*cos(re(x))*cosh(im(x)))*sin(atan2(2*(-2 + cos(re(x))*cosh(im(x)))*sin(re(x))*sinh(im(x)), cosh(im(x))^2*sin(re(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 4*cos(re(x))*cosh(im(x)))/2)^2/2 + sin(re(x))^2*cosh(2*im(x))/2 - sqrt(-32*sin(re(x))^2 + 32*cos(re(x))^2 + (-1 + cosh(2*im(x)))^2*cos(re(x))^4 + (-1 + cosh(2*im(x)))^2*sin(re(x))^4 - 8*cos(re(x))^3*cosh(3*im(x)) - 4*cos(re(x))^2*sin(re(x))^2 + 4*sin(re(x))^4*cosh(2*im(x)) + 8*cos(re(x))^3*cosh(im(x)) + 32*cos(re(x))^2*cosh(2*im(x)) + 32*sin(re(x))^2*cosh(2*im(x)) - 8*sin(re(x))^2*cos(re(x))*cosh(3*im(x)) + 2*(-1 + cosh(2*im(x)))^2*cos(re(x))^2*sin(re(x))^2 + 4*cos(re(x))^2*sin(re(x))^2*cosh(2*im(x)) + 40*sin(re(x))^2*cos(re(x))*cosh(im(x)))*cos(atan2(2*(-2 + cos(re(x))*cosh(im(x)))*sin(re(x))*sinh(im(x)), cosh(im(x))^2*sin(re(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 4*cos(re(x))*cosh(im(x)))/2)^2/2 - cos(re(x))^2*cosh(2*im(x))/2)/(4*(-cos(re(x))*cosh(im(x)) + i*sin(re(x))*sinh(im(x)))^2)

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y^2+y*tgx=1/cosx la ecuación

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