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- La ecuación:
-
Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
-
Ecuación x^2-14*x+33=0
-
Ecuación 5-x^2=0
- Expresar {x} en función de y en la ecuación:
- -9*x-12*y=-19
- -8*x+3*y=-4
- 18*x+17*y=-14
- 10*x+3*y=2
- Derivada de:
- f*(x)
-
Expresiones idénticas
- f*(x)=((nueve *x+ seis)/(ocho *x- cinco))
- f multiplicar por (x) es igual a ((9 multiplicar por x más 6) dividir por (8 multiplicar por x menos 5))
- f multiplicar por (x) es igual a ((nueve multiplicar por x más seis) dividir por (ocho multiplicar por x menos cinco))
- f(x)=((9x+6)/(8x-5))
- fx=9x+6/8x-5
- f*(x)=((9*x+6) dividir por (8*x-5))
-
Expresiones semejantes
- y*x.diff(x)+2*x=(2*y/sqrt(x))/(cos(y)^(2))
- x.diff(x)=3*x+y
- f*(x)=((9*x+6)/(8*x+5))
- x.diff(x)=y
- x2*y(x2).diff(x2).diff(x2)=(y(x2).diff(x2))*2
- f*(x)=((9*x-6)/(8*x-5))
- y*x.diff(x)+2*x=(2*y*x^(1/2))/(cos(y))^2
f*(x)=((9*x+6)/(8*x-5)) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación:
$$f x = \frac{9 x + 6}{8 x - 5}$$
Multipliquemos las dos partes de la ecuación por los denominadores:
-5 + 8*x
obtendremos:
$$f x \left(8 x - 5\right) = \frac{\left(8 x - 5\right) \left(9 x + 6\right)}{8 x - 5}$$
$$f x \left(8 x - 5\right) = 9 x + 6$$
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$f x \left(8 x - 5\right) = 9 x + 6$$
en
$$8 f x^{2} - 5 f x - 9 x - 6 = 0$$
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
$$a = 8 f$$
$$b = - 5 f - 9$$
$$c = -6$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{5 f + \sqrt{192 f + \left(- 5 f - 9\right)^{2}} + 9}{16 f}$$
$$x_{2} = \frac{5 f - \sqrt{192 f + \left(- 5 f - 9\right)^{2}} + 9}{16 f}$$
$$f x = \frac{9 x + 6}{8 x - 5}$$
Multipliquemos las dos partes de la ecuación por los denominadores:
-5 + 8*x
obtendremos:
$$f x \left(8 x - 5\right) = \frac{\left(8 x - 5\right) \left(9 x + 6\right)}{8 x - 5}$$
$$f x \left(8 x - 5\right) = 9 x + 6$$
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$f x \left(8 x - 5\right) = 9 x + 6$$
en
$$8 f x^{2} - 5 f x - 9 x - 6 = 0$$
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
$$a = 8 f$$
$$b = - 5 f - 9$$
$$c = -6$$
, entonces
D = b^2 - 4 * a * c =
(-9 - 5*f)^2 - 4 * (8*f) * (-6) = (-9 - 5*f)^2 + 192*f
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{5 f + \sqrt{192 f + \left(- 5 f - 9\right)^{2}} + 9}{16 f}$$
$$x_{2} = \frac{5 f - \sqrt{192 f + \left(- 5 f - 9\right)^{2}} + 9}{16 f}$$
Gráfica
Respuesta rápida
[src]
/ / ___________________________________________________________________________ \ / ___________________________________________________________________________ \ \ / ___________________________________________________________________________ \ / ___________________________________________________________________________ \
| | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/||
| |9 + 5*re(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *cos|-------------------------------------------------------------------------||*im(f) |5*im(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*re(f)| |5*im(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*im(f) |9 + 5*re(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *cos|-------------------------------------------------------------------------||*re(f)
| \ \ 2 // \ \ 2 // | \ \ 2 // \ \ 2 //
x1 = I*|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \
\ 16*\im (f) + re (f)/ 16*\im (f) + re (f)/ / 16*\im (f) + re (f)/ 16*\im (f) + re (f)/
$$x_{1} = \frac{\left(- \sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{16 \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(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(- \sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{im}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right) + \frac{\left(- \sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}$$
/ / ___________________________________________________________________________ \ / ___________________________________________________________________________ \ \ / ___________________________________________________________________________ \ / ___________________________________________________________________________ \
| | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/||
| |9 + 5*re(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *cos|-------------------------------------------------------------------------||*im(f) |5*im(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*re(f)| |5*im(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*im(f) |9 + 5*re(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *cos|-------------------------------------------------------------------------||*re(f)
| \ \ 2 // \ \ 2 // | \ \ 2 // \ \ 2 //
x2 = I*|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \
\ 16*\im (f) + re (f)/ 16*\im (f) + re (f)/ / 16*\im (f) + re (f)/ 16*\im (f) + re (f)/
$$x_{2} = \frac{\left(\sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{16 \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(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{im}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right) + \frac{\left(\sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}$$
x2 = (((50*re(f)*im(f) + 282*im(f))^2 + (25*re(f)^2 + 282*re(f) - 25*im(f)^2 + 81)^2)^(1/4)*sin(atan2(50*re(f)*im(f) + 282*im(f, 25*re(f)^2 + 282*re(f) - 25*im(f)^2 + 81)/2) + 5*im(f))*im(f)/(16*(re(f)^2 + im(f)^2)) + i*((((50*re(f)*im(f) + 282*im(f))^2 + (25*re(f)^2 + 282*re(f) - 25*im(f)^2 + 81)^2)^(1/4)*sin(atan2(50*re(f)*im(f) + 282*im(f), 25*re(f)^2 + 282*re(f) - 25*im(f)^2 + 81)/2) + 5*im(f))*re(f)/(16*(re(f)^2 + im(f)^2)) - (((50*re(f)*im(f) + 282*im(f))^2 + (25*re(f)^2 + 282*re(f) - 25*im(f)^2 + 81)^2)^(1/4)*cos(atan2(50*re(f)*im(f) + 282*im(f), 25*re(f)^2 + 282*re(f) - 25*im(f)^2 + 81)/2) + 5*re(f) + 9)*im(f)/(16*(re(f)^2 + im(f)^2))) + (((50*re(f)*im(f) + 282*im(f))^2 + (25*re(f)^2 + 282*re(f) - 25*im(f)^2 + 81)^2)^(1/4)*cos(atan2(50*re(f)*im(f) + 282*im(f), 25*re(f)^2 + 282*re(f) - 25*im(f)^2 + 81)/2) + 5*re(f) + 9)*re(f)/(16*(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 / / 2 2 \\| | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | |9 + 5*re(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *cos|-------------------------------------------------------------------------||*im(f) |5*im(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*re(f)| |5*im(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*im(f) |9 + 5*re(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *cos|-------------------------------------------------------------------------||*re(f) | |9 + 5*re(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *cos|-------------------------------------------------------------------------||*im(f) |5*im(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*re(f)| |5*im(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*im(f) |9 + 5*re(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*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 \ \ 16*\im (f) + re (f)/ 16*\im (f) + re (f)/ / 16*\im (f) + re (f)/ 16*\im (f) + re (f)/ \ 16*\im (f) + re (f)/ 16*\im (f) + re (f)/ / 16*\im (f) + re (f)/ 16*\im (f) + re (f)/
$$\left(\frac{\left(- \sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{16 \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(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(- \sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{im}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right) + \frac{\left(- \sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right) + \left(\frac{\left(\sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{16 \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(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{im}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right) + \frac{\left(\sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{re}{\left(f\right)}}{16 \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 2 \\| | / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | | | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | |9 + 5*re(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *cos|-------------------------------------------------------------------------||*im(f) |5*im(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*re(f)| | |9 + 5*re(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *cos|-------------------------------------------------------------------------||*im(f) |5*im(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*re(f)| |5*im(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*im(f) |5*im(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*im(f) |9 + 5*re(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *cos|-------------------------------------------------------------------------||*re(f) |9 + 5*re(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*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 \ \ 16*\im (f) + re (f)/ 16*\im (f) + re (f)/ / \ 16*\im (f) + re (f)/ 16*\im (f) + re (f)/ / 16*\im (f) + re (f)/ 16*\im (f) + re (f)/ 16*\im (f) + re (f)/ 16*\im (f) + re (f)/
$$\frac{\left(- \sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{16 \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(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(- \sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{im}{\left(f\right)}}{16 \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(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{im}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right) + \frac{\left(- \sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}$$
producto
/ / / ___________________________________________________________________________ \ / ___________________________________________________________________________ \ \ / ___________________________________________________________________________ \ / ___________________________________________________________________________ \ \ / / / ___________________________________________________________________________ \ / ___________________________________________________________________________ \ \ / ___________________________________________________________________________ \ / ___________________________________________________________________________ \ \ | | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | | | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | | | | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | 4 / 2 / 2 2 \ |atan2\282*im(f) + 50*im(f)*re(f), 81 - 25*im (f) + 25*re (f) + 282*re(f)/|| | | | |9 + 5*re(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *cos|-------------------------------------------------------------------------||*im(f) |5*im(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*re(f)| |5*im(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*im(f) |9 + 5*re(f) - \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *cos|-------------------------------------------------------------------------||*re(f)| | | |9 + 5*re(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *cos|-------------------------------------------------------------------------||*im(f) |5*im(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*re(f)| |5*im(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*re(f)/ *sin|-------------------------------------------------------------------------||*im(f) |9 + 5*re(f) + \/ (282*im(f) + 50*im(f)*re(f)) + \81 - 25*im (f) + 25*re (f) + 282*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 \ | \ \ 16*\im (f) + re (f)/ 16*\im (f) + re (f)/ / 16*\im (f) + re (f)/ 16*\im (f) + re (f)/ / \ \ 16*\im (f) + re (f)/ 16*\im (f) + re (f)/ / 16*\im (f) + re (f)/ 16*\im (f) + re (f)/ /
$$\left(\frac{\left(- \sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{16 \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(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(- \sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{im}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right) + \frac{\left(- \sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right) \left(\frac{\left(\sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{im}{\left(f\right)}}{16 \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(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{im}{\left(f\right)}\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{im}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right) + \frac{\left(\sqrt[4]{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)}\right)^{2} + \left(25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(50 \operatorname{re}{\left(f\right)} \operatorname{im}{\left(f\right)} + 282 \operatorname{im}{\left(f\right)},25 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 282 \operatorname{re}{\left(f\right)} - 25 \left(\operatorname{im}{\left(f\right)}\right)^{2} + 81 \right)}}{2} \right)} + 5 \operatorname{re}{\left(f\right)} + 9\right) \operatorname{re}{\left(f\right)}}{16 \left(\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}\right)}\right)$$
=
-3*re(f) + 3*I*im(f)
--------------------
2 2
4*im (f) + 4*re (f)
$$\frac{- 3 \operatorname{re}{\left(f\right)} + 3 i \operatorname{im}{\left(f\right)}}{4 \left(\operatorname{re}{\left(f\right)}\right)^{2} + 4 \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
(-3*re(f) + 3*i*im(f))/(4*im(f)^2 + 4*re(f)^2)