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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
- -17*x-15*y=-17
- -9*x+11*y=9
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Expresiones idénticas
- ax^ dos +(2a- cinco)x+(uno - seis)= cero
- ax al cuadrado más (2a menos 5)x más (1 menos 6) es igual a 0
- ax en el grado dos más (2a menos cinco)x más (uno menos seis) es igual a cero
- ax2+(2a-5)x+(1-6)=0
- ax2+2a-5x+1-6=0
- ax²+(2a-5)x+(1-6)=0
- ax en el grado 2+(2a-5)x+(1-6)=0
- ax^2+2a-5x+1-6=0
- ax^2+(2a-5)x+(1-6)=O
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Expresiones semejantes
- ax^2+(2a+5)x+(1-6)=0
- ax^2+(2a-5)x+(1+6)=0
- ax^2+(2a-5)x-(1-6)=0
- ax^2-(2a-5)x+(1-6)=0
-
Expresiones con funciones
- ax
- ax+by+c=0
- ax=-by-c
- ax=2a-1
- ax+√(3-2x-x^2)=4a+2
- ax=a+1+x
ax^2+(2a-5)x+(1-6)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 a*x + (2*a - 5)*x - 5 = 0
$$\left(a x^{2} + x \left(2 a - 5\right)\right) - 5 = 0$$
Solución detallada
Abramos la expresión en la ecuación
$$\left(a x^{2} + x \left(2 a - 5\right)\right) - 5 = 0$$
Obtenemos la ecuación cuadrática
$$a x^{2} + 2 a x - 5 x - 5 = 0$$
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
$$b = 2 a - 5$$
$$c = -5$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{- 2 a + \sqrt{20 a + \left(2 a - 5\right)^{2}} + 5}{2 a}$$
$$x_{2} = \frac{- 2 a - \sqrt{20 a + \left(2 a - 5\right)^{2}} + 5}{2 a}$$
$$\left(a x^{2} + x \left(2 a - 5\right)\right) - 5 = 0$$
Obtenemos la ecuación cuadrática
$$a x^{2} + 2 a x - 5 x - 5 = 0$$
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
True
$$b = 2 a - 5$$
$$c = -5$$
, entonces
D = b^2 - 4 * a * c =
(-5 + 2*a)^2 - 4 * (a) * (-5) = (-5 + 2*a)^2 + 20*a
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{- 2 a + \sqrt{20 a + \left(2 a - 5\right)^{2}} + 5}{2 a}$$
$$x_{2} = \frac{- 2 a - \sqrt{20 a + \left(2 a - 5\right)^{2}} + 5}{2 a}$$
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$a x^{2} + x \left(2 a - 5\right) - 5 = 0$$
Коэффициент при x равен
$$a$$
entonces son posibles los casos para a :
$$a < 0$$
$$a = 0$$
Consideremos todos los casos con detalles:
Con
$$a < 0$$
la ecuación será
$$- x^{2} - 7 x - 5 = 0$$
su solución
$$x = - \frac{7}{2} - \frac{\sqrt{29}}{2}$$
$$x = - \frac{7}{2} + \frac{\sqrt{29}}{2}$$
Con
$$a = 0$$
la ecuación será
$$- 5 x - 5 = 0$$
su solución
$$x = -1$$
$$a x^{2} + x \left(2 a - 5\right) - 5 = 0$$
Коэффициент при x равен
$$a$$
entonces son posibles los casos para a :
$$a < 0$$
$$a = 0$$
Consideremos todos los casos con detalles:
Con
$$a < 0$$
la ecuación será
$$- x^{2} - 7 x - 5 = 0$$
su solución
$$x = - \frac{7}{2} - \frac{\sqrt{29}}{2}$$
$$x = - \frac{7}{2} + \frac{\sqrt{29}}{2}$$
Con
$$a = 0$$
la ecuación será
$$- 5 x - 5 = 0$$
su solución
$$x = -1$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(a x^{2} + x \left(2 a - 5\right)\right) - 5 = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{a x^{2} + x \left(2 a - 5\right) - 5}{a} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{2 a - 5}{a}$$
$$q = \frac{c}{a}$$
$$q = - \frac{5}{a}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{2 a - 5}{a}$$
$$x_{1} x_{2} = - \frac{5}{a}$$
$$\left(a x^{2} + x \left(2 a - 5\right)\right) - 5 = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{a x^{2} + x \left(2 a - 5\right) - 5}{a} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{2 a - 5}{a}$$
$$q = \frac{c}{a}$$
$$q = - \frac{5}{a}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{2 a - 5}{a}$$
$$x_{1} x_{2} = - \frac{5}{a}$$
Gráfica
Respuesta rápida
[src]
// ________________________________________________ \ / ________________________________________________ \ \ / ________________________________________________ \ / ________________________________________________ \
|| / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/||
||-2*im(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*re(a) |5 - 2*re(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*im(a)| |-2*im(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*im(a) |5 - 2*re(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*re(a)
|\ \ 2 // \ \ 2 // | \ \ 2 // \ \ 2 //
x1 = I*|--------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------
| / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \
\ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / 2*\im (a) + re (a)/ 2*\im (a) + re (a)/
$$x_{1} = \frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}$$
// ________________________________________________ \ / ________________________________________________ \ \ / ________________________________________________ \ / ________________________________________________ \
|| / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/||
||-2*im(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*re(a) |5 - 2*re(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*im(a)| |-2*im(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*im(a) |5 - 2*re(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*re(a)
|\ \ 2 // \ \ 2 // | \ \ 2 // \ \ 2 //
x2 = I*|--------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------
| / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \
\ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / 2*\im (a) + re (a)/ 2*\im (a) + re (a)/
$$x_{2} = \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}$$
x2 = (((4*re(a)^2 - 4*im(a)^2 + 25)^2 + 64*re(a)^2*im(a)^2)^(1/4)*sin(atan2(8*re(a)*im(a, 4*re(a)^2 - 4*im(a)^2 + 25)/2) - 2*im(a))*im(a)/(2*(re(a)^2 + im(a)^2)) + i*((((4*re(a)^2 - 4*im(a)^2 + 25)^2 + 64*re(a)^2*im(a)^2)^(1/4)*sin(atan2(8*re(a)*im(a), 4*re(a)^2 - 4*im(a)^2 + 25)/2) - 2*im(a))*re(a)/(2*(re(a)^2 + im(a)^2)) - (((4*re(a)^2 - 4*im(a)^2 + 25)^2 + 64*re(a)^2*im(a)^2)^(1/4)*cos(atan2(8*re(a)*im(a), 4*re(a)^2 - 4*im(a)^2 + 25)/2) - 2*re(a) + 5)*im(a)/(2*(re(a)^2 + im(a)^2))) + (((4*re(a)^2 - 4*im(a)^2 + 25)^2 + 64*re(a)^2*im(a)^2)^(1/4)*cos(atan2(8*re(a)*im(a), 4*re(a)^2 - 4*im(a)^2 + 25)/2) - 2*re(a) + 5)*re(a)/(2*(re(a)^2 + im(a)^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 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| || 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| ||-2*im(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*re(a) |5 - 2*re(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*im(a)| |-2*im(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*im(a) |5 - 2*re(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*re(a) ||-2*im(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*re(a) |5 - 2*re(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*im(a)| |-2*im(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*im(a) |5 - 2*re(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*re(a) |\ \ 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 (a) + re (a)/ 2*\im (a) + re (a)/ / 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ \ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / 2*\im (a) + re (a)/ 2*\im (a) + re (a)/
$$\left(\frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \left(\frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\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 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | || 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| ||-2*im(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*re(a) |5 - 2*re(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*im(a)| ||-2*im(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*re(a) |5 - 2*re(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*im(a)| |-2*im(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*im(a) |-2*im(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*im(a) |5 - 2*re(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*re(a) |5 - 2*re(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*re(a) |\ \ 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 (a) + re (a)/ 2*\im (a) + re (a)/ / \ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/
$$\frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + i \left(\frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\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 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | | || 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 25 - 4*im (a) + 4*re (a)/|| | | ||-2*im(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*re(a) |5 - 2*re(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*im(a)| |-2*im(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*im(a) |5 - 2*re(a) - \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*re(a)| | ||-2*im(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*re(a) |5 - 2*re(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*im(a)| |-2*im(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *sin|----------------------------------------------||*im(a) |5 - 2*re(a) + \/ \25 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|----------------------------------------------||*re(a)| | |\ \ 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 (a) + re (a)/ 2*\im (a) + re (a)/ / 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / \ \ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ /
$$\left(\frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) \left(\frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 25 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 5\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right)$$
=
-5*re(a) + 5*I*im(a)
--------------------
2 2
im (a) + re (a)
$$\frac{- 5 \operatorname{re}{\left(a\right)} + 5 i \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
(-5*re(a) + 5*i*im(a))/(im(a)^2 + re(a)^2)