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Expresiones semejantes
- 1-0,2y*sinx-y^2=0
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1+0,2y*sinx-y^2=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
y 2
1 + -*sin(x) - y = 0
5
$$- y^{2} + \left(\frac{y}{5} \sin{\left(x \right)} + 1\right) = 0$$
Solución detallada
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
$$a = -1$$
$$b = \frac{\sin{\left(x \right)}}{5}$$
$$c = 1$$
, entonces
La ecuación tiene dos raíces.
o
$$y_{1} = - \frac{\sqrt{\frac{\sin^{2}{\left(x \right)}}{25} + 4}}{2} + \frac{\sin{\left(x \right)}}{10}$$
$$y_{2} = \frac{\sqrt{\frac{\sin^{2}{\left(x \right)}}{25} + 4}}{2} + \frac{\sin{\left(x \right)}}{10}$$
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
$$a = -1$$
$$b = \frac{\sin{\left(x \right)}}{5}$$
$$c = 1$$
, entonces
D = b^2 - 4 * a * c =
(sin(x)/5)^2 - 4 * (-1) * (1) = 4 + sin(x)^2/25
La ecuación tiene dos raíces.
y1 = (-b + sqrt(D)) / (2*a)
y2 = (-b - sqrt(D)) / (2*a)
o
$$y_{1} = - \frac{\sqrt{\frac{\sin^{2}{\left(x \right)}}{25} + 4}}{2} + \frac{\sin{\left(x \right)}}{10}$$
$$y_{2} = \frac{\sqrt{\frac{\sin^{2}{\left(x \right)}}{25} + 4}}{2} + \frac{\sin{\left(x \right)}}{10}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$- y^{2} + \left(\frac{y}{5} \sin{\left(x \right)} + 1\right) = 0$$
de
$$a y^{2} + b y + c = 0$$
como ecuación cuadrática reducida
$$y^{2} + \frac{b y}{a} + \frac{c}{a} = 0$$
$$y^{2} - \frac{y \sin{\left(x \right)}}{5} - 1 = 0$$
$$p y + q + y^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{\sin{\left(x \right)}}{5}$$
$$q = \frac{c}{a}$$
$$q = -1$$
Fórmulas de Cardano-Vieta
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = \frac{\sin{\left(x \right)}}{5}$$
$$y_{1} y_{2} = -1$$
$$- y^{2} + \left(\frac{y}{5} \sin{\left(x \right)} + 1\right) = 0$$
de
$$a y^{2} + b y + c = 0$$
como ecuación cuadrática reducida
$$y^{2} + \frac{b y}{a} + \frac{c}{a} = 0$$
$$y^{2} - \frac{y \sin{\left(x \right)}}{5} - 1 = 0$$
$$p y + q + y^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{\sin{\left(x \right)}}{5}$$
$$q = \frac{c}{a}$$
$$q = -1$$
Fórmulas de Cardano-Vieta
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = \frac{\sin{\left(x \right)}}{5}$$
$$y_{1} y_{2} = -1$$
Gráfica
Respuesta rápida
[src]
/ ____________________________________________________________________________________________________________________ \ ____________________________________________________________________________________________________________________
| / 2 / / 2 2 2 2 \\ | / 2 / / 2 2 2 2 \\
| 4 / / 2 2 2 2 \ 2 2 2 2 |atan2\2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/| | 4 / / 2 2 2 2 \ 2 2 2 2 |atan2\2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/|
| \/ \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ + 4*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x)) *sin|-----------------------------------------------------------------------------------------------------------------| | \/ \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ + 4*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x)) *cos|-----------------------------------------------------------------------------------------------------------------|
| \ 2 / cos(re(x))*sinh(im(x))| \ 2 / cosh(im(x))*sin(re(x))
y1 = I*|- ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------| - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------
\ 10 10 / 10 10
$$y_{1} = i \left(- \frac{\sqrt[4]{\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)} + 100\right)^{2} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}} \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)},\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)} + 100 \right)}}{2} \right)}}{10} + \frac{\cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{10}\right) - \frac{\sqrt[4]{\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)} + 100\right)^{2} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}} \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)},\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)} + 100 \right)}}{2} \right)}}{10} + \frac{\sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{10}$$
/ ____________________________________________________________________________________________________________________ \ ____________________________________________________________________________________________________________________
| / 2 / / 2 2 2 2 \\ | / 2 / / 2 2 2 2 \\
|4 / / 2 2 2 2 \ 2 2 2 2 |atan2\2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/| | 4 / / 2 2 2 2 \ 2 2 2 2 |atan2\2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/|
|\/ \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ + 4*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x)) *sin|-----------------------------------------------------------------------------------------------------------------| | \/ \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ + 4*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x)) *cos|-----------------------------------------------------------------------------------------------------------------|
| \ 2 / cos(re(x))*sinh(im(x))| \ 2 / cosh(im(x))*sin(re(x))
y2 = I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------
\ 10 10 / 10 10
$$y_{2} = i \left(\frac{\sqrt[4]{\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)} + 100\right)^{2} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}} \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)},\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)} + 100 \right)}}{2} \right)}}{10} + \frac{\cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{10}\right) + \frac{\sqrt[4]{\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)} + 100\right)^{2} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}} \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)},\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)} + 100 \right)}}{2} \right)}}{10} + \frac{\sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{10}$$
y2 = i*(((sin(re(x))^2*cosh(im(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 100)^2 + 4*sin(re(x))^2*cos(re(x))^2*sinh(im(x))^2*cosh(im(x))^2)^(1/4)*sin(atan2(2*sin(re(x))*cos(re(x))*sinh(im(x))*cosh(im(x), sin(re(x))^2*cosh(im(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 100)/2)/10 + cos(re(x))*sinh(im(x))/10) + ((sin(re(x))^2*cosh(im(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 100)^2 + 4*sin(re(x))^2*cos(re(x))^2*sinh(im(x))^2*cosh(im(x))^2)^(1/4)*cos(atan2(2*sin(re(x))*cos(re(x))*sinh(im(x))*cosh(im(x)), sin(re(x))^2*cosh(im(x))^2 - cos(re(x))^2*sinh(im(x))^2 + 100)/2)/10 + sin(re(x))*cosh(im(x))/10)
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 \\ | 4 / / 2 2 2 2 \ 2 2 2 2 |atan2\2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/| | 4 / / 2 2 2 2 \ 2 2 2 2 |atan2\2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/| |4 / / 2 2 2 2 \ 2 2 2 2 |atan2\2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/| | 4 / / 2 2 2 2 \ 2 2 2 2 |atan2\2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/| | \/ \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ + 4*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x)) *sin|-----------------------------------------------------------------------------------------------------------------| | \/ \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ + 4*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x)) *cos|-----------------------------------------------------------------------------------------------------------------| |\/ \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ + 4*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x)) *sin|-----------------------------------------------------------------------------------------------------------------| | \/ \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ + 4*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x)) *cos|-----------------------------------------------------------------------------------------------------------------| | \ 2 / cos(re(x))*sinh(im(x))| \ 2 / cosh(im(x))*sin(re(x)) | \ 2 / cos(re(x))*sinh(im(x))| \ 2 / cosh(im(x))*sin(re(x)) I*|- ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------| - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------- + I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------- \ 10 10 / 10 10 \ 10 10 / 10 10
$$\left(i \left(- \frac{\sqrt[4]{\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)} + 100\right)^{2} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}} \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)},\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)} + 100 \right)}}{2} \right)}}{10} + \frac{\cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{10}\right) - \frac{\sqrt[4]{\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)} + 100\right)^{2} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}} \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)},\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)} + 100 \right)}}{2} \right)}}{10} + \frac{\sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{10}\right) + \left(i \left(\frac{\sqrt[4]{\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)} + 100\right)^{2} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}} \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)},\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)} + 100 \right)}}{2} \right)}}{10} + \frac{\cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{10}\right) + \frac{\sqrt[4]{\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)} + 100\right)^{2} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}} \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)},\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)} + 100 \right)}}{2} \right)}}{10} + \frac{\sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{10}\right)$$
=
/ ____________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________ \ | / 2 / / 2 2 2 2 \\ | | / 2 / / 2 2 2 2 \\ | | 4 / / 2 2 2 2 \ 2 2 2 2 |atan2\2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/| | |4 / / 2 2 2 2 \ 2 2 2 2 |atan2\2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/| | | \/ \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ + 4*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x)) *sin|-----------------------------------------------------------------------------------------------------------------| | |\/ \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ + 4*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x)) *sin|-----------------------------------------------------------------------------------------------------------------| | | \ 2 / cos(re(x))*sinh(im(x))| | \ 2 / cos(re(x))*sinh(im(x))| cosh(im(x))*sin(re(x)) I*|- ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------| + I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------| + ---------------------- \ 10 10 / \ 10 10 / 5
$$i \left(- \frac{\sqrt[4]{\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)} + 100\right)^{2} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}} \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)},\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)} + 100 \right)}}{2} \right)}}{10} + \frac{\cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{10}\right) + i \left(\frac{\sqrt[4]{\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)} + 100\right)^{2} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}} \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)},\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)} + 100 \right)}}{2} \right)}}{10} + \frac{\cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{10}\right) + \frac{\sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{5}$$
producto
/ / ____________________________________________________________________________________________________________________ \ ____________________________________________________________________________________________________________________ \ / / ____________________________________________________________________________________________________________________ \ ____________________________________________________________________________________________________________________ \ | | / 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 2 2 2 |atan2\2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/| | 4 / / 2 2 2 2 \ 2 2 2 2 |atan2\2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/| | | |4 / / 2 2 2 2 \ 2 2 2 2 |atan2\2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/| | 4 / / 2 2 2 2 \ 2 2 2 2 |atan2\2*cos(re(x))*cosh(im(x))*sin(re(x))*sinh(im(x)), 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/| | | | \/ \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ + 4*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x)) *sin|-----------------------------------------------------------------------------------------------------------------| | \/ \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ + 4*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x)) *cos|-----------------------------------------------------------------------------------------------------------------| | | |\/ \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ + 4*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x)) *sin|-----------------------------------------------------------------------------------------------------------------| | \/ \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ + 4*cos (re(x))*cosh (im(x))*sin (re(x))*sinh (im(x)) *cos|-----------------------------------------------------------------------------------------------------------------| | | | \ 2 / cos(re(x))*sinh(im(x))| \ 2 / cosh(im(x))*sin(re(x))| | | \ 2 / cos(re(x))*sinh(im(x))| \ 2 / cosh(im(x))*sin(re(x))| |I*|- ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------| - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------|*|I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------| \ \ 10 10 / 10 10 / \ \ 10 10 / 10 10 /
$$\left(i \left(- \frac{\sqrt[4]{\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)} + 100\right)^{2} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}} \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)},\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)} + 100 \right)}}{2} \right)}}{10} + \frac{\cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{10}\right) - \frac{\sqrt[4]{\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)} + 100\right)^{2} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}} \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)},\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)} + 100 \right)}}{2} \right)}}{10} + \frac{\sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{10}\right) \left(i \left(\frac{\sqrt[4]{\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)} + 100\right)^{2} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}} \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)},\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)} + 100 \right)}}{2} \right)}}{10} + \frac{\cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}}{10}\right) + \frac{\sqrt[4]{\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)} + 100\right)^{2} + 4 \sin^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \cos^{2}{\left(\operatorname{re}{\left(x\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\right)} \right)}} \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)},\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)} + 100 \right)}}{2} \right)}}{10} + \frac{\sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}}{10}\right)$$
=
/ / ______________________________________________________________________________________________________________ / /sin(2*re(x))*sinh(2*im(x)) 2 2 2 2 \\ \ ______________________________________________________________________________________________________________ / /sin(2*re(x))*sinh(2*im(x)) 2 2 2 2 \\ \ / / ______________________________________________________________________________________________________________ / /sin(2*re(x))*sinh(2*im(x)) 2 2 2 2 \\ \ ______________________________________________________________________________________________________________ / /sin(2*re(x))*sinh(2*im(x)) 2 2 2 2 \\ \
| | / 2 2 2 |atan2|--------------------------, 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))|| | / 2 2 2 |atan2|--------------------------, 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))|| | | | / 2 2 2 |atan2|--------------------------, 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))|| | / 2 2 2 |atan2|--------------------------, 100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))|| |
| | / / 2 2 2 2 \ cosh (im(x))*sinh (im(x))*(-1 + cos(4*re(x))) | \ 2 /| | / / 2 2 2 2 \ cosh (im(x))*sinh (im(x))*(-1 + cos(4*re(x))) | \ 2 /| | | | / / 2 2 2 2 \ cosh (im(x))*sinh (im(x))*(-1 + cos(4*re(x))) | \ 2 /| | / / 2 2 2 2 \ cosh (im(x))*sinh (im(x))*(-1 + cos(4*re(x))) | \ 2 /| |
-|I*|4 / \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ - --------------------------------------------- *sin|--------------------------------------------------------------------------------------------| + cos(re(x))*sinh(im(x))| + 4 / \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ - --------------------------------------------- *cos|--------------------------------------------------------------------------------------------| + cosh(im(x))*sin(re(x))|*|I*|4 / \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ - --------------------------------------------- *sin|--------------------------------------------------------------------------------------------| - cos(re(x))*sinh(im(x))| + 4 / \100 + cosh (im(x))*sin (re(x)) - cos (re(x))*sinh (im(x))/ - --------------------------------------------- *cos|--------------------------------------------------------------------------------------------| - cosh(im(x))*sin(re(x))|
\ \\/ 2 \ 2 / / \/ 2 \ 2 / / \ \\/ 2 \ 2 / / \/ 2 \ 2 / /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
100
$$- \frac{\left(i \left(\sqrt[4]{- \frac{\left(\cos{\left(4 \operatorname{re}{\left(x\right)} \right)} - 1\right) \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\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)} + 100\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sin{\left(2 \operatorname{re}{\left(x\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(x\right)} \right)}}{2},\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)} + 100 \right)}}{2} \right)} - \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) + \sqrt[4]{- \frac{\left(\cos{\left(4 \operatorname{re}{\left(x\right)} \right)} - 1\right) \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\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)} + 100\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sin{\left(2 \operatorname{re}{\left(x\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(x\right)} \right)}}{2},\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)} + 100 \right)}}{2} \right)} - \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right) \left(i \left(\sqrt[4]{- \frac{\left(\cos{\left(4 \operatorname{re}{\left(x\right)} \right)} - 1\right) \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\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)} + 100\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sin{\left(2 \operatorname{re}{\left(x\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(x\right)} \right)}}{2},\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)} + 100 \right)}}{2} \right)} + \cos{\left(\operatorname{re}{\left(x\right)} \right)} \sinh{\left(\operatorname{im}{\left(x\right)} \right)}\right) + \sqrt[4]{- \frac{\left(\cos{\left(4 \operatorname{re}{\left(x\right)} \right)} - 1\right) \sinh^{2}{\left(\operatorname{im}{\left(x\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(x\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)} + 100\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sin{\left(2 \operatorname{re}{\left(x\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(x\right)} \right)}}{2},\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)} + 100 \right)}}{2} \right)} + \sin{\left(\operatorname{re}{\left(x\right)} \right)} \cosh{\left(\operatorname{im}{\left(x\right)} \right)}\right)}{100}$$
-(i*(((100 + cosh(im(x))^2*sin(re(x))^2 - cos(re(x))^2*sinh(im(x))^2)^2 - cosh(im(x))^2*sinh(im(x))^2*(-1 + cos(4*re(x)))/2)^(1/4)*sin(atan2(sin(2*re(x))*sinh(2*im(x))/2, 100 + cosh(im(x))^2*sin(re(x))^2 - cos(re(x))^2*sinh(im(x))^2)/2) + cos(re(x))*sinh(im(x))) + ((100 + cosh(im(x))^2*sin(re(x))^2 - cos(re(x))^2*sinh(im(x))^2)^2 - cosh(im(x))^2*sinh(im(x))^2*(-1 + cos(4*re(x)))/2)^(1/4)*cos(atan2(sin(2*re(x))*sinh(2*im(x))/2, 100 + cosh(im(x))^2*sin(re(x))^2 - cos(re(x))^2*sinh(im(x))^2)/2) + cosh(im(x))*sin(re(x)))*(i*(((100 + cosh(im(x))^2*sin(re(x))^2 - cos(re(x))^2*sinh(im(x))^2)^2 - cosh(im(x))^2*sinh(im(x))^2*(-1 + cos(4*re(x)))/2)^(1/4)*sin(atan2(sin(2*re(x))*sinh(2*im(x))/2, 100 + cosh(im(x))^2*sin(re(x))^2 - cos(re(x))^2*sinh(im(x))^2)/2) - cos(re(x))*sinh(im(x))) + ((100 + cosh(im(x))^2*sin(re(x))^2 - cos(re(x))^2*sinh(im(x))^2)^2 - cosh(im(x))^2*sinh(im(x))^2*(-1 + cos(4*re(x)))/2)^(1/4)*cos(atan2(sin(2*re(x))*sinh(2*im(x))/2, 100 + cosh(im(x))^2*sin(re(x))^2 - cos(re(x))^2*sinh(im(x))^2)/2) - cosh(im(x))*sin(re(x)))/100