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- La ecuación:
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Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
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Ecuación x^2+4=5x
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Ecuación x(x^2+2x+1)=6(x+1)
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Ecuación 4x+1=-3x+15
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 13*x-12*y=19
- -9*x+11*y=9
- -4*x-8*y=-20
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Expresiones idénticas
- f(x+ uno)^ dos +3f(x+ uno)- diez = cero
- f(x más 1) al cuadrado más 3f(x más 1) menos 10 es igual a 0
- f(x más uno) en el grado dos más 3f(x más uno) menos diez es igual a cero
- f(x+1)2+3f(x+1)-10=0
- fx+12+3fx+1-10=0
- f(x+1)²+3f(x+1)-10=0
- f(x+1) en el grado 2+3f(x+1)-10=0
- fx+1^2+3fx+1-10=0
- f(x+1)^2+3f(x+1)-10=O
-
Expresiones semejantes
- f(x+1)^2+3f(x-1)-10=0
- f(x-1)^2+3f(x+1)-10=0
- f(x+1)^2+3f(x+1)+10=0
- f(x+1)^2-3f(x+1)-10=0
f(x+1)^2+3f(x+1)-10=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
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
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
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{- 5 f + \sqrt{25 f^{2} - 4 f \left(4 f - 10\right)}}{2 f}$$
$$x_{2} = \frac{- 5 f - \sqrt{25 f^{2} - 4 f \left(4 f - 10\right)}}{2 f}$$
$$\left(f \left(x + 1\right)^{2} + 3 f \left(x + 1\right)\right) - 10 = 0$$
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]
// ________________________________________________________________________________ \ / ________________________________________________________________________________ \ \ / ________________________________________________________________________________ \ / ________________________________________________________________________________ \
|| / 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*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)))