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f(x+1)^2+3f(x+1)-10=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
         2                       
f*(x + 1)  + 3*f*(x + 1) - 10 = 0
$$\left(f \left(x + 1\right)^{2} + 3 f \left(x + 1\right)\right) - 10 = 0$$
Solución detallada
Abramos la expresión en la ecuación
$$\left(f \left(x + 1\right)^{2} + 3 f \left(x + 1\right)\right) - 10 = 0$$
Obtenemos la ecuación cuadrática
$$f x^{2} + 5 f x + 4 f - 10 = 0$$
Es la ecuación de la forma
a*x^2 + b*x + c = 0

La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = f$$
$$b = 5 f$$
$$c = 4 f - 10$$
, entonces
D = b^2 - 4 * a * c = 

(5*f)^2 - 4 * (f) * (-10 + 4*f) = 25*f^2 - 4*f*(-10 + 4*f)

La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

o
$$x_{1} = \frac{- 5 f + \sqrt{25 f^{2} - 4 f \left(4 f - 10\right)}}{2 f}$$
$$x_{2} = \frac{- 5 f - \sqrt{25 f^{2} - 4 f \left(4 f - 10\right)}}{2 f}$$
Gráfica
Respuesta rápida [src]
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       ||           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||      |   |           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||      
       ||-5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*re(f)   |-5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*im(f)|   |-5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*im(f)   |-5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*re(f)
       |\                                                                                                   \                                      2                                       //         \                                                                                                   \                                      2                                       //      |   \                                                                                                   \                                      2                                       //         \                                                                                                   \                                      2                                       //      
x1 = I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
       |                                                                                      /  2        2   \                                                                                                                                                                             /  2        2   \                                                                                    |                                                                                         /  2        2   \                                                                                                                                                                             /  2        2   \                                                                                    
       \                                                                                    2*\im (f) + re (f)/                                                                                                                                                                           2*\im (f) + re (f)/                                                                                    /                                                                                       2*\im (f) + re (f)/                                                                                                                                                                           2*\im (f) + re (f)/                                                                                    
$$x_{1} = \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{re}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + i \left(\frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{re}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right)$$
       //              ________________________________________________________________________________                                                                                    \         /              ________________________________________________________________________________                                                                                    \      \   /              ________________________________________________________________________________                                                                                    \         /              ________________________________________________________________________________                                                                                    \      
       ||             /                                    2                                               /     /                                            2                          \\|         |             /                                    2                                               /     /                                            2                          \\|      |   |             /                                    2                                               /     /                                            2                          \\|         |             /                                    2                                               /     /                                            2                          \\|      
       ||          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||      |   |          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||      
       ||5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*im(f)   |5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*re(f)|   |5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*im(f)   |5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*re(f)
       |\                                                                                                  \                                      2                                       //         \                                                                                                  \                                      2                                       //      |   \                                                                                                  \                                      2                                       //         \                                                                                                  \                                      2                                       //      
x2 = I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
       |                                                                                     /  2        2   \                                                                                                                                                                            /  2        2   \                                                                                    |                                                                                        /  2        2   \                                                                                                                                                                            /  2        2   \                                                                                    
       \                                                                                   2*\im (f) + re (f)/                                                                                                                                                                          2*\im (f) + re (f)/                                                                                    /                                                                                      2*\im (f) + re (f)/                                                                                                                                                                          2*\im (f) + re (f)/                                                                                    
$$x_{2} = - \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + i \left(- \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right)$$
x2 = -((((9*re(f) + 40)*re(f) - 9*im(f)^2)^2 + ((9*re(f) + 40)*im(f) + 9*re(f)*im(f))^2)^(1/4)*sin(atan2((9*re(f) + 40)*im(f) + 9*re(f)*im(f, (9*re(f) + 40)*re(f) - 9*im(f)^2)/2) + 5*im(f))*im(f)/(2*(re(f)^2 + im(f)^2)) - ((((9*re(f) + 40)*re(f) - 9*im(f)^2)^2 + ((9*re(f) + 40)*im(f) + 9*re(f)*im(f))^2)^(1/4)*cos(atan2((9*re(f) + 40)*im(f) + 9*re(f)*im(f), (9*re(f) + 40)*re(f) - 9*im(f)^2)/2) + 5*re(f))*re(f)/(2*(re(f)^2 + im(f)^2)) + i*(-((((9*re(f) + 40)*re(f) - 9*im(f)^2)^2 + ((9*re(f) + 40)*im(f) + 9*re(f)*im(f))^2)^(1/4)*sin(atan2((9*re(f) + 40)*im(f) + 9*re(f)*im(f), (9*re(f) + 40)*re(f) - 9*im(f)^2)/2) + 5*im(f))*re(f)/(2*(re(f)^2 + im(f)^2)) + ((((9*re(f) + 40)*re(f) - 9*im(f)^2)^2 + ((9*re(f) + 40)*im(f) + 9*re(f)*im(f))^2)^(1/4)*cos(atan2((9*re(f) + 40)*im(f) + 9*re(f)*im(f), (9*re(f) + 40)*re(f) - 9*im(f)^2)/2) + 5*re(f))*im(f)/(2*(re(f)^2 + im(f)^2))))
Suma y producto de raíces [src]
suma
  //               ________________________________________________________________________________                                                                                    \         /               ________________________________________________________________________________                                                                                    \      \   /               ________________________________________________________________________________                                                                                    \         /               ________________________________________________________________________________                                                                                    \           //              ________________________________________________________________________________                                                                                    \         /              ________________________________________________________________________________                                                                                    \      \   /              ________________________________________________________________________________                                                                                    \         /              ________________________________________________________________________________                                                                                    \      
  ||              /                                    2                                               /     /                                            2                          \\|         |              /                                    2                                               /     /                                            2                          \\|      |   |              /                                    2                                               /     /                                            2                          \\|         |              /                                    2                                               /     /                                            2                          \\|           ||             /                                    2                                               /     /                                            2                          \\|         |             /                                    2                                               /     /                                            2                          \\|      |   |             /                                    2                                               /     /                                            2                          \\|         |             /                                    2                                               /     /                                            2                          \\|      
  ||           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||      |   |           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||           ||          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||      |   |          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||      
  ||-5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*re(f)   |-5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*im(f)|   |-5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*im(f)   |-5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*re(f)     ||5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*im(f)   |5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*re(f)|   |5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*im(f)   |5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*re(f)
  |\                                                                                                   \                                      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*\im (f) + re (f)/                                                                                                                                                                           2*\im (f) + re (f)/                                                                                    /                                                                                       2*\im (f) + re (f)/                                                                                                                                                                           2*\im (f) + re (f)/                                                                                         \                                                                                   2*\im (f) + re (f)/                                                                                                                                                                          2*\im (f) + re (f)/                                                                                    /                                                                                      2*\im (f) + re (f)/                                                                                                                                                                          2*\im (f) + re (f)/                                                                                    
$$\left(\frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{re}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + i \left(\frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{re}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right)\right) + \left(- \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + i \left(- \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right)\right)$$
=
  //               ________________________________________________________________________________                                                                                    \         /               ________________________________________________________________________________                                                                                    \      \     //              ________________________________________________________________________________                                                                                    \         /              ________________________________________________________________________________                                                                                    \      \   /               ________________________________________________________________________________                                                                                    \         /               ________________________________________________________________________________                                                                                    \         /              ________________________________________________________________________________                                                                                    \         /              ________________________________________________________________________________                                                                                    \      
  ||              /                                    2                                               /     /                                            2                          \\|         |              /                                    2                                               /     /                                            2                          \\|      |     ||             /                                    2                                               /     /                                            2                          \\|         |             /                                    2                                               /     /                                            2                          \\|      |   |              /                                    2                                               /     /                                            2                          \\|         |              /                                    2                                               /     /                                            2                          \\|         |             /                                    2                                               /     /                                            2                          \\|         |             /                                    2                                               /     /                                            2                          \\|      
  ||           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||      |     ||          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||      |   |           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||      
  ||-5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*re(f)   |-5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*im(f)|     ||5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*im(f)   |5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*re(f)|   |-5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*im(f)   |-5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*re(f)   |5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*im(f)   |5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*re(f)
  |\                                                                                                   \                                      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*\im (f) + re (f)/                                                                                                                                                                           2*\im (f) + re (f)/                                                                                    /     \                                                                                   2*\im (f) + re (f)/                                                                                                                                                                          2*\im (f) + re (f)/                                                                                    /                                                                                       2*\im (f) + re (f)/                                                                                                                                                                           2*\im (f) + re (f)/                                                                                                                                                                          2*\im (f) + re (f)/                                                                                                                                                                          2*\im (f) + re (f)/                                                                                    
$$\frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{re}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + i \left(\frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{re}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right) + i \left(- \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right)$$
producto
/  //               ________________________________________________________________________________                                                                                    \         /               ________________________________________________________________________________                                                                                    \      \   /               ________________________________________________________________________________                                                                                    \         /               ________________________________________________________________________________                                                                                    \      \ /  //              ________________________________________________________________________________                                                                                    \         /              ________________________________________________________________________________                                                                                    \      \   /              ________________________________________________________________________________                                                                                    \         /              ________________________________________________________________________________                                                                                    \      \
|  ||              /                                    2                                               /     /                                            2                          \\|         |              /                                    2                                               /     /                                            2                          \\|      |   |              /                                    2                                               /     /                                            2                          \\|         |              /                                    2                                               /     /                                            2                          \\|      | |  ||             /                                    2                                               /     /                                            2                          \\|         |             /                                    2                                               /     /                                            2                          \\|      |   |             /                                    2                                               /     /                                            2                          \\|         |             /                                    2                                               /     /                                            2                          \\|      |
|  ||           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||      |   |           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |           4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||      | |  ||          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||      |   |          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||         |          4 /  /      2                          \                                          2     |atan2\(40 + 9*re(f))*im(f) + 9*im(f)*re(f), - 9*im (f) + (40 + 9*re(f))*re(f)/||      |
|  ||-5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*re(f)   |-5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*im(f)|   |-5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*im(f)   |-5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*re(f)| |  ||5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*im(f)   |5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*re(f)|   |5*im(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *sin|------------------------------------------------------------------------------||*im(f)   |5*re(f) + \/   \- 9*im (f) + (40 + 9*re(f))*re(f)/  + ((40 + 9*re(f))*im(f) + 9*im(f)*re(f))  *cos|------------------------------------------------------------------------------||*re(f)|
|  |\                                                                                                   \                                      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*\im (f) + re (f)/                                                                                                                                                                           2*\im (f) + re (f)/                                                                                    /                                                                                       2*\im (f) + re (f)/                                                                                                                                                                           2*\im (f) + re (f)/                                                                                    / \  \                                                                                   2*\im (f) + re (f)/                                                                                                                                                                          2*\im (f) + re (f)/                                                                                    /                                                                                      2*\im (f) + re (f)/                                                                                                                                                                          2*\im (f) + re (f)/                                                                                    /
$$\left(\frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{re}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + i \left(\frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} - 5 \operatorname{re}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right)\right) \left(- \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + i \left(- \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)^{2} + \left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{im}{\left(f\right)} + 9 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)},\left(9 \operatorname{re}{\left(f\right)} + 40\right) \operatorname{re}{\left(f\right)} - 9 \left(\operatorname{im}{\left(f\right)}\right)^{2} \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{2 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right)\right)$$
=
                                                                                                                _______________________________________________________________________________________________________               _______________________________________________________________________________________________________                _______________________________________________________________________________________________________             _________________    __________________________________________    _______________________________________________________________________________________________________         _________________    __________________________________________              _________________    __________________________________________               _________________    __________________________________________                  _________________    __________________________________________    _______________________________________________________________________________________________________      
         2             2            3           4           4            2                  2      2           /      4           4            3             2             2            2      2            2                        /      4           4            3             2             2            2      2            2             2           /      4           4            3             2             2            2      2            2             2        /   2        2       /             2           2                   /      4           4            3             2             2            2      2            2                  /   2        2       /             2           2                             /   2        2       /             2           2                   2          /   2        2       /             2           2                   2           4 /   2        2     4 /             2           2                 4 /      4           4            3             2             2            2      2            2                
- 1600*im (f) - 1600*re (f) - 720*re (f) - 81*im (f) - 81*re (f) - 720*im (f)*re(f) - 162*im (f)*re (f) - 40*\/  81*im (f) + 81*re (f) + 720*re (f) + 1600*im (f) + 1600*re (f) + 162*im (f)*re (f) + 720*im (f)*re(f) *re(f) + 41*\/  81*im (f) + 81*re (f) + 720*re (f) + 1600*im (f) + 1600*re (f) + 162*im (f)*re (f) + 720*im (f)*re(f) *im (f) + 41*\/  81*im (f) + 81*re (f) + 720*re (f) + 1600*im (f) + 1600*re (f) + 162*im (f)*re (f) + 720*im (f)*re(f) *re (f) + \/  im (f) + re (f) *\/  1600 + 81*im (f) + 81*re (f) + 720*re(f) *\/  81*im (f) + 81*re (f) + 720*re (f) + 1600*im (f) + 1600*re (f) + 162*im (f)*re (f) + 720*im (f)*re(f)  - 40*\/  im (f) + re (f) *\/  1600 + 81*im (f) + 81*re (f) + 720*re(f) *re(f) - 9*\/  im (f) + re (f) *\/  1600 + 81*im (f) + 81*re (f) + 720*re(f) *im (f) - 9*\/  im (f) + re (f) *\/  1600 + 81*im (f) + 81*re (f) + 720*re(f) *re (f) + 80*I*\/  im (f) + re (f) *\/  1600 + 81*im (f) + 81*re (f) + 720*re(f) *\/  81*im (f) + 81*re (f) + 720*re (f) + 1600*im (f) + 1600*re (f) + 162*im (f)*re (f) + 720*im (f)*re(f) *im(f)
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   /  2        2   \   /      4           4            3             2             2            2      2            2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 8*\im (f) + re (f)/*\/  81*im (f) + 81*re (f) + 720*re (f) + 1600*im (f) + 1600*re (f) + 162*im (f)*re (f) + 720*im (f)*re(f)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
$$\frac{80 i \sqrt[4]{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sqrt[4]{81 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 720 \operatorname{re}{\left(f\right)} + 81 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 1600} \sqrt[4]{81 \left(\operatorname{re}{\left(f\right)}\right)^{4} + 720 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 162 \left(\operatorname{re}{\left(f\right)}\right)^{2} \left(\operatorname{im}{\left(f\right)}\right)^{2} + 1600 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 720 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \left(\operatorname{im}{\left(f\right)}\right)^{4} + 1600 \left(\operatorname{im}{\left(f\right)}\right)^{2}} \operatorname{im}{\left(f\right)} + \sqrt{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sqrt{81 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 720 \operatorname{re}{\left(f\right)} + 81 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 1600} \sqrt{81 \left(\operatorname{re}{\left(f\right)}\right)^{4} + 720 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 162 \left(\operatorname{re}{\left(f\right)}\right)^{2} \left(\operatorname{im}{\left(f\right)}\right)^{2} + 1600 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 720 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \left(\operatorname{im}{\left(f\right)}\right)^{4} + 1600 \left(\operatorname{im}{\left(f\right)}\right)^{2}} - 9 \sqrt{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sqrt{81 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 720 \operatorname{re}{\left(f\right)} + 81 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 1600} \left(\operatorname{re}{\left(f\right)}\right)^{2} - 40 \sqrt{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sqrt{81 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 720 \operatorname{re}{\left(f\right)} + 81 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 1600} \operatorname{re}{\left(f\right)} - 9 \sqrt{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} \sqrt{81 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 720 \operatorname{re}{\left(f\right)} + 81 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 1600} \left(\operatorname{im}{\left(f\right)}\right)^{2} + 41 \sqrt{81 \left(\operatorname{re}{\left(f\right)}\right)^{4} + 720 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 162 \left(\operatorname{re}{\left(f\right)}\right)^{2} \left(\operatorname{im}{\left(f\right)}\right)^{2} + 1600 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 720 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \left(\operatorname{im}{\left(f\right)}\right)^{4} + 1600 \left(\operatorname{im}{\left(f\right)}\right)^{2}} \left(\operatorname{re}{\left(f\right)}\right)^{2} - 40 \sqrt{81 \left(\operatorname{re}{\left(f\right)}\right)^{4} + 720 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 162 \left(\operatorname{re}{\left(f\right)}\right)^{2} \left(\operatorname{im}{\left(f\right)}\right)^{2} + 1600 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 720 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \left(\operatorname{im}{\left(f\right)}\right)^{4} + 1600 \left(\operatorname{im}{\left(f\right)}\right)^{2}} \operatorname{re}{\left(f\right)} + 41 \sqrt{81 \left(\operatorname{re}{\left(f\right)}\right)^{4} + 720 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 162 \left(\operatorname{re}{\left(f\right)}\right)^{2} \left(\operatorname{im}{\left(f\right)}\right)^{2} + 1600 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 720 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \left(\operatorname{im}{\left(f\right)}\right)^{4} + 1600 \left(\operatorname{im}{\left(f\right)}\right)^{2}} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 81 \left(\operatorname{re}{\left(f\right)}\right)^{4} - 720 \left(\operatorname{re}{\left(f\right)}\right)^{3} - 162 \left(\operatorname{re}{\left(f\right)}\right)^{2} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 1600 \left(\operatorname{re}{\left(f\right)}\right)^{2} - 720 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} - 81 \left(\operatorname{im}{\left(f\right)}\right)^{4} - 1600 \left(\operatorname{im}{\left(f\right)}\right)^{2}}{8 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right) \sqrt{81 \left(\operatorname{re}{\left(f\right)}\right)^{4} + 720 \left(\operatorname{re}{\left(f\right)}\right)^{3} + 162 \left(\operatorname{re}{\left(f\right)}\right)^{2} \left(\operatorname{im}{\left(f\right)}\right)^{2} + 1600 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 720 \operatorname{re}{\left(f\right)} \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \left(\operatorname{im}{\left(f\right)}\right)^{4} + 1600 \left(\operatorname{im}{\left(f\right)}\right)^{2}}}$$
(-1600*im(f)^2 - 1600*re(f)^2 - 720*re(f)^3 - 81*im(f)^4 - 81*re(f)^4 - 720*im(f)^2*re(f) - 162*im(f)^2*re(f)^2 - 40*sqrt(81*im(f)^4 + 81*re(f)^4 + 720*re(f)^3 + 1600*im(f)^2 + 1600*re(f)^2 + 162*im(f)^2*re(f)^2 + 720*im(f)^2*re(f))*re(f) + 41*sqrt(81*im(f)^4 + 81*re(f)^4 + 720*re(f)^3 + 1600*im(f)^2 + 1600*re(f)^2 + 162*im(f)^2*re(f)^2 + 720*im(f)^2*re(f))*im(f)^2 + 41*sqrt(81*im(f)^4 + 81*re(f)^4 + 720*re(f)^3 + 1600*im(f)^2 + 1600*re(f)^2 + 162*im(f)^2*re(f)^2 + 720*im(f)^2*re(f))*re(f)^2 + sqrt(im(f)^2 + re(f)^2)*sqrt(1600 + 81*im(f)^2 + 81*re(f)^2 + 720*re(f))*sqrt(81*im(f)^4 + 81*re(f)^4 + 720*re(f)^3 + 1600*im(f)^2 + 1600*re(f)^2 + 162*im(f)^2*re(f)^2 + 720*im(f)^2*re(f)) - 40*sqrt(im(f)^2 + re(f)^2)*sqrt(1600 + 81*im(f)^2 + 81*re(f)^2 + 720*re(f))*re(f) - 9*sqrt(im(f)^2 + re(f)^2)*sqrt(1600 + 81*im(f)^2 + 81*re(f)^2 + 720*re(f))*im(f)^2 - 9*sqrt(im(f)^2 + re(f)^2)*sqrt(1600 + 81*im(f)^2 + 81*re(f)^2 + 720*re(f))*re(f)^2 + 80*i*(im(f)^2 + re(f)^2)^(1/4)*(1600 + 81*im(f)^2 + 81*re(f)^2 + 720*re(f))^(1/4)*(81*im(f)^4 + 81*re(f)^4 + 720*re(f)^3 + 1600*im(f)^2 + 1600*re(f)^2 + 162*im(f)^2*re(f)^2 + 720*im(f)^2*re(f))^(1/4)*im(f))/(8*(im(f)^2 + re(f)^2)*sqrt(81*im(f)^4 + 81*re(f)^4 + 720*re(f)^3 + 1600*im(f)^2 + 1600*re(f)^2 + 162*im(f)^2*re(f)^2 + 720*im(f)^2*re(f)))