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ax+√(3-2x-x^2)=4a+2 la ecuación
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Solución
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/ 2
a*x + \/ 3 - 2*x - x = 4*a + 2
$$a x + \sqrt{- x^{2} + \left(3 - 2 x\right)} = 4 a + 2$$
Solución detallada
Tenemos la ecuación
$$a x + \sqrt{- x^{2} + \left(3 - 2 x\right)} = 4 a + 2$$
$$\sqrt{- x^{2} - 2 x + 3} = - a x + 4 a + 2$$
Elevemos las dos partes de la ecuación a la potencia 2
$$- x^{2} - 2 x + 3 = \left(- a x + 4 a + 2\right)^{2}$$
$$- x^{2} - 2 x + 3 = a^{2} x^{2} - 8 a^{2} x + 16 a^{2} - 4 a x + 16 a + 4$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- a^{2} x^{2} + 8 a^{2} x - 16 a^{2} + 4 a x - 16 a - x^{2} - 2 x - 1 = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = - a^{2} - 1$$
$$b = 8 a^{2} + 4 a - 2$$
$$c = - 16 a^{2} - 16 a - 1$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{- 8 a^{2} - 4 a + \sqrt{- \left(- 4 a^{2} - 4\right) \left(- 16 a^{2} - 16 a - 1\right) + \left(8 a^{2} + 4 a - 2\right)^{2}} + 2}{- 2 a^{2} - 2}$$
$$x_{2} = \frac{- 8 a^{2} - 4 a - \sqrt{- \left(- 4 a^{2} - 4\right) \left(- 16 a^{2} - 16 a - 1\right) + \left(8 a^{2} + 4 a - 2\right)^{2}} + 2}{- 2 a^{2} - 2}$$
$$a x + \sqrt{- x^{2} + \left(3 - 2 x\right)} = 4 a + 2$$
$$\sqrt{- x^{2} - 2 x + 3} = - a x + 4 a + 2$$
Elevemos las dos partes de la ecuación a la potencia 2
$$- x^{2} - 2 x + 3 = \left(- a x + 4 a + 2\right)^{2}$$
$$- x^{2} - 2 x + 3 = a^{2} x^{2} - 8 a^{2} x + 16 a^{2} - 4 a x + 16 a + 4$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- a^{2} x^{2} + 8 a^{2} x - 16 a^{2} + 4 a x - 16 a - x^{2} - 2 x - 1 = 0$$
Es la ecuación de la forma
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = - a^{2} - 1$$
$$b = 8 a^{2} + 4 a - 2$$
$$c = - 16 a^{2} - 16 a - 1$$
, entonces
D = b^2 - 4 * a * c =
(-2 + 4*a + 8*a^2)^2 - 4 * (-1 - a^2) * (-1 - 16*a - 16*a^2) = (-2 + 4*a + 8*a^2)^2 - (-4 - 4*a^2)*(-1 - 16*a - 16*a^2)
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{- 8 a^{2} - 4 a + \sqrt{- \left(- 4 a^{2} - 4\right) \left(- 16 a^{2} - 16 a - 1\right) + \left(8 a^{2} + 4 a - 2\right)^{2}} + 2}{- 2 a^{2} - 2}$$
$$x_{2} = \frac{- 8 a^{2} - 4 a - \sqrt{- \left(- 4 a^{2} - 4\right) \left(- 16 a^{2} - 16 a - 1\right) + \left(8 a^{2} + 4 a - 2\right)^{2}} + 2}{- 2 a^{2} - 2}$$
Gráfica
Respuesta rápida
[src]
/ / ___________________________________________________________________________________ \ / ___________________________________________________________________________________ \ \ / ___________________________________________________________________________________ \ / ___________________________________________________________________________________ \
| | / 2 / / 2 \\ | | / 2 / / 2 \\| | | / 2 / / 2 \\| | / 2 / / 2 \\ |
|/ 2 2 \ | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| | | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | / 2 2 \ | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| |
|\1 + re (a) - im (a)/*|2*im(a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)| 2*|-1 - 4*im (a) + 2*re(a) + 4*re (a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------||*im(a)*re(a)| \1 + re (a) - im (a)/*|-1 - 4*im (a) + 2*re(a) + 4*re (a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------|| 2*|2*im(a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)|*im(a)*re(a)
| \ \ 2 / / \ \ 2 // | \ \ 2 // \ \ 2 / /
x1 = I*|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 2 | 2 2
| / 2 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2
\ \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a) / \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a)
$$x_{1} = i \left(\frac{\left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{2 \left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{2 \left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right) \left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
/ / ___________________________________________________________________________________ \ / ___________________________________________________________________________________ \ \ / ___________________________________________________________________________________ \ / ___________________________________________________________________________________ \
| | / 2 / / 2 \\ | | / 2 / / 2 \\| | | / 2 / / 2 \\| | / 2 / / 2 \\ |
|/ 2 2 \ | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| | | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | / 2 2 \ | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| |
|\1 + re (a) - im (a)/*|2*im(a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)| 2*|-1 - 4*im (a) + 2*re(a) + 4*re (a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------||*im(a)*re(a)| \1 + re (a) - im (a)/*|-1 - 4*im (a) + 2*re(a) + 4*re (a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------|| 2*|2*im(a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)|*im(a)*re(a)
| \ \ 2 / / \ \ 2 // | \ \ 2 // \ \ 2 / /
x2 = I*|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 2 | 2 2
| / 2 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2
\ \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a) / \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a)
$$x_{2} = i \left(\frac{\left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{2 \left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{2 \left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right) \left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
x2 = i*((((-(21*re(a) + 20)*re(a) + 21*im(a)^2)^2 + (-(21*re(a) + 20)*im(a) - 21*re(a)*im(a))^2)^(1/4)*sin(atan2(-(21*re(a) + 20)*im(a) - 21*re(a)*im(a, -(21*re(a) + 20)*re(a) + 21*im(a)^2)/2) + 8*re(a)*im(a) + 2*im(a))*(re(a)^2 - im(a)^2 + 1)/((re(a)^2 - im(a)^2 + 1)^2 + 4*re(a)^2*im(a)^2) - 2*(((-(21*re(a) + 20)*re(a) + 21*im(a)^2)^2 + (-(21*re(a) + 20)*im(a) - 21*re(a)*im(a))^2)^(1/4)*cos(atan2(-(21*re(a) + 20)*im(a) - 21*re(a)*im(a), -(21*re(a) + 20)*re(a) + 21*im(a)^2)/2) + 4*re(a)^2 + 2*re(a) - 4*im(a)^2 - 1)*re(a)*im(a)/((re(a)^2 - im(a)^2 + 1)^2 + 4*re(a)^2*im(a)^2)) + 2*(((-(21*re(a) + 20)*re(a) + 21*im(a)^2)^2 + (-(21*re(a) + 20)*im(a) - 21*re(a)*im(a))^2)^(1/4)*sin(atan2(-(21*re(a) + 20)*im(a) - 21*re(a)*im(a), -(21*re(a) + 20)*re(a) + 21*im(a)^2)/2) + 8*re(a)*im(a) + 2*im(a))*re(a)*im(a)/((re(a)^2 - im(a)^2 + 1)^2 + 4*re(a)^2*im(a)^2) + (re(a)^2 - im(a)^2 + 1)*(((-(21*re(a) + 20)*re(a) + 21*im(a)^2)^2 + (-(21*re(a) + 20)*im(a) - 21*re(a)*im(a))^2)^(1/4)*cos(atan2(-(21*re(a) + 20)*im(a) - 21*re(a)*im(a), -(21*re(a) + 20)*re(a) + 21*im(a)^2)/2) + 4*re(a)^2 + 2*re(a) - 4*im(a)^2 - 1)/((re(a)^2 - im(a)^2 + 1)^2 + 4*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 \ | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| | | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | / 2 2 \ | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| | |/ 2 2 \ | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| | | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | / 2 2 \ | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| | |\1 + re (a) - im (a)/*|2*im(a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)| 2*|-1 - 4*im (a) + 2*re(a) + 4*re (a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------||*im(a)*re(a)| \1 + re (a) - im (a)/*|-1 - 4*im (a) + 2*re(a) + 4*re (a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------|| 2*|2*im(a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)|*im(a)*re(a) |\1 + re (a) - im (a)/*|2*im(a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)| 2*|-1 - 4*im (a) + 2*re(a) + 4*re (a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------||*im(a)*re(a)| \1 + re (a) - im (a)/*|-1 - 4*im (a) + 2*re(a) + 4*re (a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------|| 2*|2*im(a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)|*im(a)*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 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2 \ \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a) / \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a) \ \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a) / \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a)
$$\left(i \left(\frac{\left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{2 \left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{2 \left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right) \left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \left(i \left(\frac{\left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{2 \left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{2 \left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right) \left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \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 \\| | / 2 / / 2 \\ | | / 2 / / 2 \\ | |/ 2 2 \ | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| | | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | |/ 2 2 \ | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| | | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | / 2 2 \ | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| / 2 2 \ | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| | |\1 + re (a) - im (a)/*|2*im(a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)| 2*|-1 - 4*im (a) + 2*re(a) + 4*re (a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------||*im(a)*re(a)| |\1 + re (a) - im (a)/*|2*im(a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)| 2*|-1 - 4*im (a) + 2*re(a) + 4*re (a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------||*im(a)*re(a)| \1 + re (a) - im (a)/*|-1 - 4*im (a) + 2*re(a) + 4*re (a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------|| \1 + re (a) - im (a)/*|-1 - 4*im (a) + 2*re(a) + 4*re (a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------|| 2*|2*im(a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)|*im(a)*re(a) 2*|2*im(a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)|*im(a)*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 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 \ \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a) / \ \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a) / \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a)
$$i \left(\frac{\left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{2 \left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + i \left(\frac{\left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{2 \left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{2 \left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{2 \left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right) \left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right) \left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
producto
/ / / ___________________________________________________________________________________ \ / ___________________________________________________________________________________ \ \ / ___________________________________________________________________________________ \ / ___________________________________________________________________________________ \ \ / / / ___________________________________________________________________________________ \ / ___________________________________________________________________________________ \ \ / ___________________________________________________________________________________ \ / ___________________________________________________________________________________ \ \ | | | / 2 / / 2 \\ | | / 2 / / 2 \\| | | / 2 / / 2 \\| | / 2 / / 2 \\ | | | | | / 2 / / 2 \\ | | / 2 / / 2 \\| | | / 2 / / 2 \\| | / 2 / / 2 \\ | | | |/ 2 2 \ | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| | | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | / 2 2 \ | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| | | | |/ 2 2 \ | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| | | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | / 2 2 \ | 2 2 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/|| | 4 / / 2 \ 2 |atan2\-(20 + 21*re(a))*im(a) - 21*im(a)*re(a), 21*im (a) - (20 + 21*re(a))*re(a)/| | | | |\1 + re (a) - im (a)/*|2*im(a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)| 2*|-1 - 4*im (a) + 2*re(a) + 4*re (a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------||*im(a)*re(a)| \1 + re (a) - im (a)/*|-1 - 4*im (a) + 2*re(a) + 4*re (a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------|| 2*|2*im(a) - \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)|*im(a)*re(a)| | |\1 + re (a) - im (a)/*|2*im(a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)| 2*|-1 - 4*im (a) + 2*re(a) + 4*re (a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------||*im(a)*re(a)| \1 + re (a) - im (a)/*|-1 - 4*im (a) + 2*re(a) + 4*re (a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *cos|---------------------------------------------------------------------------------|| 2*|2*im(a) + \/ \21*im (a) - (20 + 21*re(a))*re(a)/ + (-(20 + 21*re(a))*im(a) - 21*im(a)*re(a)) *sin|---------------------------------------------------------------------------------| + 8*im(a)*re(a)|*im(a)*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 2 \ 2 2 / 2 2 \ 2 2 | | | / 2 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2 | \ \ \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a) / \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a) / \ \ \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a) / \1 + re (a) - im (a)/ + 4*im (a)*re (a) \1 + re (a) - im (a)/ + 4*im (a)*re (a) /
$$\left(i \left(\frac{\left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{2 \left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{2 \left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right) \left(- \sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) \left(i \left(\frac{\left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{2 \left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{2 \left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right) \left(\sqrt[4]{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{im}{\left(a\right)} - 21 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},- \left(21 \operatorname{re}{\left(a\right)} + 20\right) \operatorname{re}{\left(a\right)} + 21 \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right)$$
=
2 4 3 4 2 3 2 2 2 2
1 - 17*im (a) + 16*im (a) + 16*re (a) + 16*re (a) + 16*re(a) + 17*re (a) - 16*I*im (a) + 16*I*im(a) + 16*im (a)*re(a) + 32*im (a)*re (a) - 16*I*re (a)*im(a) + 30*I*im(a)*re(a)
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4 4 2 2 2 2
1 + im (a) + re (a) - 2*im (a) + 2*re (a) + 2*im (a)*re (a)
$$\frac{16 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} + 32 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 16 i \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} + 17 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 30 i \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 16 \operatorname{re}{\left(a\right)} + 16 \left(\operatorname{im}{\left(a\right)}\right)^{4} - 16 i \left(\operatorname{im}{\left(a\right)}\right)^{3} - 17 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 16 i \operatorname{im}{\left(a\right)} + 1}{\left(\operatorname{re}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} - 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1}$$
(1 - 17*im(a)^2 + 16*im(a)^4 + 16*re(a)^3 + 16*re(a)^4 + 16*re(a) + 17*re(a)^2 - 16*i*im(a)^3 + 16*i*im(a) + 16*im(a)^2*re(a) + 32*im(a)^2*re(a)^2 - 16*i*re(a)^2*im(a) + 30*i*im(a)*re(a))/(1 + im(a)^4 + re(a)^4 - 2*im(a)^2 + 2*re(a)^2 + 2*im(a)^2*re(a)^2)