Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación x^4+2*x^2-8=0
-
Ecuación x*(x^2+8*x+16)=5*(x+4)
-
Ecuación -25-x=-17
-
Ecuación x^2+3x=4
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -14*x+10*y=19
- -9*x+1*y=3
- -17*x+1*y=-11
- 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
- (1/cos(x)^2)=0
- y-1/cos(x)=0
- 1/sin(x)-1/cos(x)=0
- (1/((cos(x))^3+(sin(x))^3))^2+2*((3cos(x)sin(x)((cos(x)-sin(x))))/((cos(x))^3+(sin(x))^3))^2-3((sin(x))^6+(cos(x))^6-2(sin(x))(cos(x))^5+4(sin(x))^2(cos(x))^4-10(sin(x))^3(cos(x))^3+4(sin(x))^4(cos(x))^2-2(sin(x))^5(cos(x)))/((cos(x))^3+(sin(x))^3)^3=0
- y^2-y*tgx=1/cosx
-
Expresiones con funciones
- tgx
- tgx=x+2
- tgx=1/(2tg15)
- tgx=1/(sqrt(8)-3)+sqrt(8)
- tgx=3/2
- tgx=-sqrt(2)-1/sqrt(2)-1
- cosx
- cosx/2=1/2
- cosx-2sinx=|cosx|
- cosx=-3√2
- cosx/1+sinx=0
- cosx3=-12
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)
$$y^{2} + y \tan{\left(x \right)} = \frac{1}{\cos{\left(x \right)}}$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$y^{2} + y \tan{\left(x \right)} = \frac{1}{\cos{\left(x \right)}}$$
en
$$\left(y^{2} + y \tan{\left(x \right)}\right) - \frac{1}{\cos{\left(x \right)}} = 0$$
Es la ecuación de la forma
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
La ecuación tiene dos raíces.
o
$$y_{1} = \frac{\sqrt{\tan^{2}{\left(x \right)} + \frac{4}{\cos{\left(x \right)}}}}{2} - \frac{\tan{\left(x \right)}}{2}$$
$$y_{2} = - \frac{\sqrt{\tan^{2}{\left(x \right)} + \frac{4}{\cos{\left(x \right)}}}}{2} - \frac{\tan{\left(x \right)}}{2}$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$y^{2} + y \tan{\left(x \right)} = \frac{1}{\cos{\left(x \right)}}$$
en
$$\left(y^{2} + y \tan{\left(x \right)}\right) - \frac{1}{\cos{\left(x \right)}} = 0$$
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)
o
$$y_{1} = \frac{\sqrt{\tan^{2}{\left(x \right)} + \frac{4}{\cos{\left(x \right)}}}}{2} - \frac{\tan{\left(x \right)}}{2}$$
$$y_{2} = - \frac{\sqrt{\tan^{2}{\left(x \right)} + \frac{4}{\cos{\left(x \right)}}}}{2} - \frac{\tan{\left(x \right)}}{2}$$
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
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = - \tan{\left(x \right)}$$
$$y_{1} y_{2} = - \frac{1}{\cos{\left(x \right)}}$$
$$p y + q + y^{2} = 0$$
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
// ____________________________________________________________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________________________________________________________ \ \ / ____________________________________________________________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________________________________________________________ \ / / ____________________________________________________________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________________________________________________________ \ \ / ____________________________________________________________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________________________________________________________ \ || / 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*|- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | / 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*\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 / / 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))|*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)) |\ \ 2 / / \ \ 2 / / | | \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / / \ \ 2 / / \ \ 2 / / I*|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | / 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*\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
/ // ____________________________________________________________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________________________________________________________ \ \ / ____________________________________________________________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________________________________________________________ \ \ / / / ____________________________________________________________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________________________________________________________ \ \ / ____________________________________________________________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________________________________________________________ \ \ | || / 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*|- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | | / 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*\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
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
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)