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a*x^2+(2a-7)*x+5a-3=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 a*x + (2*a - 7)*x + 5*a - 3 = 0
$$\left(5 a + \left(a x^{2} + x \left(2 a - 7\right)\right)\right) - 3 = 0$$
Solución detallada
Abramos la expresión en la ecuación
$$\left(5 a + \left(a x^{2} + x \left(2 a - 7\right)\right)\right) - 3 = 0$$
Obtenemos la ecuación cuadrática
$$a x^{2} + 2 a x + 5 a - 7 x - 3 = 0$$
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
$$b = 2 a - 7$$
$$c = 5 a - 3$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{- 2 a + \sqrt{- 4 a \left(5 a - 3\right) + \left(2 a - 7\right)^{2}} + 7}{2 a}$$
$$x_{2} = \frac{- 2 a - \sqrt{- 4 a \left(5 a - 3\right) + \left(2 a - 7\right)^{2}} + 7}{2 a}$$
$$\left(5 a + \left(a x^{2} + x \left(2 a - 7\right)\right)\right) - 3 = 0$$
Obtenemos la ecuación cuadrática
$$a x^{2} + 2 a x + 5 a - 7 x - 3 = 0$$
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
$$b = 2 a - 7$$
$$c = 5 a - 3$$
, entonces
D = b^2 - 4 * a * c =
(-7 + 2*a)^2 - 4 * (a) * (-3 + 5*a) = (-7 + 2*a)^2 - 4*a*(-3 + 5*a)
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{- 2 a + \sqrt{- 4 a \left(5 a - 3\right) + \left(2 a - 7\right)^{2}} + 7}{2 a}$$
$$x_{2} = \frac{- 2 a - \sqrt{- 4 a \left(5 a - 3\right) + \left(2 a - 7\right)^{2}} + 7}{2 a}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(5 a + \left(a x^{2} + x \left(2 a - 7\right)\right)\right) - 3 = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{a x^{2} + 5 a + x \left(2 a - 7\right) - 3}{a} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{2 a - 7}{a}$$
$$q = \frac{c}{a}$$
$$q = \frac{5 a - 3}{a}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{2 a - 7}{a}$$
$$x_{1} x_{2} = \frac{5 a - 3}{a}$$
$$\left(5 a + \left(a x^{2} + x \left(2 a - 7\right)\right)\right) - 3 = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{a x^{2} + 5 a + x \left(2 a - 7\right) - 3}{a} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{2 a - 7}{a}$$
$$q = \frac{c}{a}$$
$$q = \frac{5 a - 3}{a}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{2 a - 7}{a}$$
$$x_{1} x_{2} = \frac{5 a - 3}{a}$$
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$a x^{2} + 5 a + x \left(2 a - 7\right) - 3 = 0$$
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
$$- x^{2} - 9 x - 8 = 0$$
su solución
$$x = -8$$
$$x = -1$$
Con
$$a = 0$$
la ecuación será
$$- 7 x - 3 = 0$$
su solución
$$x = - \frac{3}{7}$$
$$a x^{2} + 5 a + x \left(2 a - 7\right) - 3 = 0$$
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
$$- x^{2} - 9 x - 8 = 0$$
su solución
$$x = -8$$
$$x = -1$$
Con
$$a = 0$$
la ecuación será
$$- 7 x - 3 = 0$$
su solución
$$x = - \frac{3}{7}$$
Gráfica
Respuesta rápida
[src]
// __________________________________________________________________________ \ / __________________________________________________________________________ \ \ / __________________________________________________________________________ \ / __________________________________________________________________________ \
|| / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
|| 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/||
||-2*im(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*re(a) |7 - 2*re(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *cos|------------------------------------------------------------------------||*im(a)| |-2*im(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*im(a) |7 - 2*re(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/||
||-2*im(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*re(a) |7 - 2*re(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *cos|------------------------------------------------------------------------||*im(a)| |-2*im(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*im(a) |7 - 2*re(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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 = (((-32*re(a)*im(a) - 16*im(a))^2 + (-16*re(a)^2 - 16*re(a) + 16*im(a)^2 + 49)^2)^(1/4)*sin(atan2(-32*re(a)*im(a) - 16*im(a, -16*re(a)^2 - 16*re(a) + 16*im(a)^2 + 49)/2) - 2*im(a))*im(a)/(2*(re(a)^2 + im(a)^2)) + i*((((-32*re(a)*im(a) - 16*im(a))^2 + (-16*re(a)^2 - 16*re(a) + 16*im(a)^2 + 49)^2)^(1/4)*sin(atan2(-32*re(a)*im(a) - 16*im(a), -16*re(a)^2 - 16*re(a) + 16*im(a)^2 + 49)/2) - 2*im(a))*re(a)/(2*(re(a)^2 + im(a)^2)) - (((-32*re(a)*im(a) - 16*im(a))^2 + (-16*re(a)^2 - 16*re(a) + 16*im(a)^2 + 49)^2)^(1/4)*cos(atan2(-32*re(a)*im(a) - 16*im(a), -16*re(a)^2 - 16*re(a) + 16*im(a)^2 + 49)/2) - 2*re(a) + 7)*im(a)/(2*(re(a)^2 + im(a)^2))) + (((-32*re(a)*im(a) - 16*im(a))^2 + (-16*re(a)^2 - 16*re(a) + 16*im(a)^2 + 49)^2)^(1/4)*cos(atan2(-32*re(a)*im(a) - 16*im(a), -16*re(a)^2 - 16*re(a) + 16*im(a)^2 + 49)/2) - 2*re(a) + 7)*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 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| || 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| ||-2*im(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*re(a) |7 - 2*re(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *cos|------------------------------------------------------------------------||*im(a)| |-2*im(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*im(a) |7 - 2*re(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *cos|------------------------------------------------------------------------||*re(a) ||-2*im(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*re(a) |7 - 2*re(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *cos|------------------------------------------------------------------------||*im(a)| |-2*im(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*im(a) |7 - 2*re(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | || 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| ||-2*im(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*re(a) |7 - 2*re(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *cos|------------------------------------------------------------------------||*im(a)| ||-2*im(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*re(a) |7 - 2*re(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *cos|------------------------------------------------------------------------||*im(a)| |-2*im(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*im(a) |-2*im(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*im(a) |7 - 2*re(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *cos|------------------------------------------------------------------------||*re(a) |7 - 2*re(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | | || 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(a) - 32*im(a)*re(a), 49 - 16*re (a) - 16*re(a) + 16*im (a)/|| | | ||-2*im(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*re(a) |7 - 2*re(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *cos|------------------------------------------------------------------------||*im(a)| |-2*im(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*im(a) |7 - 2*re(a) - \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *cos|------------------------------------------------------------------------||*re(a)| | ||-2*im(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*re(a) |7 - 2*re(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *cos|------------------------------------------------------------------------||*im(a)| |-2*im(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (a)/ *sin|------------------------------------------------------------------------||*im(a) |7 - 2*re(a) + \/ (-16*im(a) - 32*im(a)*re(a)) + \49 - 16*re (a) - 16*re(a) + 16*im (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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 32 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(a\right)},- 16 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \right)}}{2} \right)} - 2 \operatorname{re}{\left(a\right)} + 7\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
-3*re(a) + 5*im (a) + 5*re (a) + 3*I*im(a)
------------------------------------------
2 2
im (a) + re (a)
$$\frac{5 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 3 \operatorname{re}{\left(a\right)} + 5 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 3 i \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
(-3*re(a) + 5*im(a)^2 + 5*re(a)^2 + 3*i*im(a))/(im(a)^2 + re(a)^2)