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pi*n^4+pi*n^3/2+x^2*(pi*n+pi/2)-2*x=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3
4 pi*n 2 / pi\
pi*n + ----- + x *|pi*n + --| - 2*x = 0
2 \ 2 /
$$- 2 x + \left(x^{2} \left(\pi n + \frac{\pi}{2}\right) + \left(\pi n^{4} + \frac{\pi n^{3}}{2}\right)\right) = 0$$
Solución detallada
Abramos la expresión en la ecuación
$$- 2 x + \left(x^{2} \left(\pi n + \frac{\pi}{2}\right) + \left(\pi n^{4} + \frac{\pi n^{3}}{2}\right)\right) = 0$$
Obtenemos la ecuación cuadrática
$$\pi n^{4} + \frac{\pi n^{3}}{2} + \pi n x^{2} + \frac{\pi x^{2}}{2} - 2 x = 0$$
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
$$a = \pi n + \frac{\pi}{2}$$
$$b = -2$$
$$c = \pi n^{4} + \frac{\pi n^{3}}{2}$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{\sqrt{- \left(4 \pi n + 2 \pi\right) \left(\pi n^{4} + \frac{\pi n^{3}}{2}\right) + 4} + 2}{2 \pi n + \pi}$$
$$x_{2} = \frac{2 - \sqrt{- \left(4 \pi n + 2 \pi\right) \left(\pi n^{4} + \frac{\pi n^{3}}{2}\right) + 4}}{2 \pi n + \pi}$$
$$- 2 x + \left(x^{2} \left(\pi n + \frac{\pi}{2}\right) + \left(\pi n^{4} + \frac{\pi n^{3}}{2}\right)\right) = 0$$
Obtenemos la ecuación cuadrática
$$\pi n^{4} + \frac{\pi n^{3}}{2} + \pi n x^{2} + \frac{\pi x^{2}}{2} - 2 x = 0$$
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
$$a = \pi n + \frac{\pi}{2}$$
$$b = -2$$
$$c = \pi n^{4} + \frac{\pi n^{3}}{2}$$
, entonces
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (pi/2 + pi*n) * (pi*n^4 + pi*n^3/2) = 4 - (2*pi + 4*pi*n)*(pi*n^4 + pi*n^3/2)
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{\sqrt{- \left(4 \pi n + 2 \pi\right) \left(\pi n^{4} + \frac{\pi n^{3}}{2}\right) + 4} + 2}{2 \pi n + \pi}$$
$$x_{2} = \frac{2 - \sqrt{- \left(4 \pi n + 2 \pi\right) \left(\pi n^{4} + \frac{\pi n^{3}}{2}\right) + 4}}{2 \pi n + \pi}$$
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$\pi n^{4} + \frac{\pi n^{3}}{2} + x^{2} \left(\pi n + \frac{\pi}{2}\right) - 2 x = 0$$
Коэффициент при x равен
$$\pi n + \frac{\pi}{2}$$
entonces son posibles los casos para n :
$$n < - \frac{1}{2}$$
$$n = - \frac{1}{2}$$
Consideremos todos los casos con detalles:
Con
$$n < - \frac{1}{2}$$
la ecuación será
$$x^{2} \left(- \frac{3 \pi}{2} + \frac{\pi}{2}\right) - 2 x + \frac{27 \pi}{8} = 0$$
su solución
$$x = \frac{-1 + \frac{\sqrt{16 + 54 \pi^{2}}}{4}}{\pi}$$
$$x = - \frac{1 + \frac{\sqrt{16 + 54 \pi^{2}}}{4}}{\pi}$$
Con
$$n = - \frac{1}{2}$$
la ecuación será
$$x^{2} \left(- \frac{\pi}{2} + \frac{\pi}{2}\right) - 2 x = 0$$
su solución
$$x = 0$$
$$\pi n^{4} + \frac{\pi n^{3}}{2} + x^{2} \left(\pi n + \frac{\pi}{2}\right) - 2 x = 0$$
Коэффициент при x равен
$$\pi n + \frac{\pi}{2}$$
entonces son posibles los casos para n :
$$n < - \frac{1}{2}$$
$$n = - \frac{1}{2}$$
Consideremos todos los casos con detalles:
Con
$$n < - \frac{1}{2}$$
la ecuación será
$$x^{2} \left(- \frac{3 \pi}{2} + \frac{\pi}{2}\right) - 2 x + \frac{27 \pi}{8} = 0$$
su solución
$$x = \frac{-1 + \frac{\sqrt{16 + 54 \pi^{2}}}{4}}{\pi}$$
$$x = - \frac{1 + \frac{\sqrt{16 + 54 \pi^{2}}}{4}}{\pi}$$
Con
$$n = - \frac{1}{2}$$
la ecuación será
$$x^{2} \left(- \frac{\pi}{2} + \frac{\pi}{2}\right) - 2 x = 0$$
su solución
$$x = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$- 2 x + \left(x^{2} \left(\pi n + \frac{\pi}{2}\right) + \left(\pi n^{4} + \frac{\pi n^{3}}{2}\right)\right) = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{\pi n^{4} + \frac{\pi n^{3}}{2} + x^{2} \left(\pi n + \frac{\pi}{2}\right) - 2 x}{\pi n + \frac{\pi}{2}} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{2}{\pi n + \frac{\pi}{2}}$$
$$q = \frac{c}{a}$$
$$q = \frac{\pi n^{4} + \frac{\pi n^{3}}{2}}{\pi n + \frac{\pi}{2}}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{2}{\pi n + \frac{\pi}{2}}$$
$$x_{1} x_{2} = \frac{\pi n^{4} + \frac{\pi n^{3}}{2}}{\pi n + \frac{\pi}{2}}$$
$$- 2 x + \left(x^{2} \left(\pi n + \frac{\pi}{2}\right) + \left(\pi n^{4} + \frac{\pi n^{3}}{2}\right)\right) = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{\pi n^{4} + \frac{\pi n^{3}}{2} + x^{2} \left(\pi n + \frac{\pi}{2}\right) - 2 x}{\pi n + \frac{\pi}{2}} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{2}{\pi n + \frac{\pi}{2}}$$
$$q = \frac{c}{a}$$
$$q = \frac{\pi n^{4} + \frac{\pi n^{3}}{2}}{\pi n + \frac{\pi}{2}}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{2}{\pi n + \frac{\pi}{2}}$$
$$x_{1} x_{2} = \frac{\pi n^{4} + \frac{\pi n^{3}}{2}}{\pi n + \frac{\pi}{2}}$$
Gráfica
Respuesta rápida
[src]
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| | / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\| / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\| | / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\| / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\
| | 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//|| 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//|| | 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//|| 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//|
| 2*|2 - \/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *cos|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||*im(n) \/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *(1 + 2*re(n))*sin|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| (1 + 2*re(n))*|2 - \/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *cos|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| 2*\/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *im(n)*sin|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| \ \ 2 // \ 2 /| \ \ 2 // \ 2 /
x1 = I*|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \
\ pi*\(1 + 2*re(n)) + 4*im (n)/ pi*\(1 + 2*re(n)) + 4*im (n)/ / pi*\(1 + 2*re(n)) + 4*im (n)/ pi*\(1 + 2*re(n)) + 4*im (n)/
$$x_{1} = \frac{\left(- \sqrt[4]{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right)\right)^{2} + \left(- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right),- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4 \right)}}{2} \right)} + 2\right) \left(2 \operatorname{re}{\left(n\right)} + 1\right)}{\pi \left(\left(2 \operatorname{re}{\left(n\right)} + 1\right)^{2} + 4 \left(\operatorname{im}{\left(n\right)}\right)^{2}\right)} + i \left(- \frac{2 \left(- \sqrt[4]{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right)\right)^{2} + \left(- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right),- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4 \right)}}{2} \right)} + 2\right) \operatorname{im}{\left(n\right)}}{\pi \left(\left(2 \operatorname{re}{\left(n\right)} + 1\right)^{2} + 4 \left(\operatorname{im}{\left(n\right)}\right)^{2}\right)} - \frac{\sqrt[4]{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right)\right)^{2} + \left(- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4\right)^{2}} \left(2 \operatorname{re}{\left(n\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right),- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4 \right)}}{2} \right)}}{\pi \left(\left(2 \operatorname{re}{\left(n\right)} + 1\right)^{2} + 4 \left(\operatorname{im}{\left(n\right)}\right)^{2}\right)}\right) - \frac{2 \sqrt[4]{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right)\right)^{2} + \left(- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right),- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4 \right)}}{2} \right)} \operatorname{im}{\left(n\right)}}{\pi \left(\left(2 \operatorname{re}{\left(n\right)} + 1\right)^{2} + 4 \left(\operatorname{im}{\left(n\right)}\right)^{2}\right)}$$
/ / _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \ _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \ / _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \ _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
| | / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\| / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\| | / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\| / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\
| | 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//|| 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//|| | 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//|| 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//|
| 2*|2 + \/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *cos|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||*im(n) \/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *(1 + 2*re(n))*sin|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| (1 + 2*re(n))*|2 + \/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *cos|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| 2*\/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *im(n)*sin|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| \ \ 2 // \ 2 /| \ \ 2 // \ 2 /
x2 = I*|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \
\ pi*\(1 + 2*re(n)) + 4*im (n)/ pi*\(1 + 2*re(n)) + 4*im (n)/ / pi*\(1 + 2*re(n)) + 4*im (n)/ pi*\(1 + 2*re(n)) + 4*im (n)/
$$x_{2} = \frac{\left(\sqrt[4]{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right)\right)^{2} + \left(- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right),- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4 \right)}}{2} \right)} + 2\right) \left(2 \operatorname{re}{\left(n\right)} + 1\right)}{\pi \left(\left(2 \operatorname{re}{\left(n\right)} + 1\right)^{2} + 4 \left(\operatorname{im}{\left(n\right)}\right)^{2}\right)} + i \left(- \frac{2 \left(\sqrt[4]{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right)\right)^{2} + \left(- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right),- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4 \right)}}{2} \right)} + 2\right) \operatorname{im}{\left(n\right)}}{\pi \left(\left(2 \operatorname{re}{\left(n\right)} + 1\right)^{2} + 4 \left(\operatorname{im}{\left(n\right)}\right)^{2}\right)} + \frac{\sqrt[4]{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right)\right)^{2} + \left(- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4\right)^{2}} \left(2 \operatorname{re}{\left(n\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right),- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4 \right)}}{2} \right)}}{\pi \left(\left(2 \operatorname{re}{\left(n\right)} + 1\right)^{2} + 4 \left(\operatorname{im}{\left(n\right)}\right)^{2}\right)}\right) + \frac{2 \sqrt[4]{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right)\right)^{2} + \left(- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \pi^{2} \left(3 \left(\operatorname{re}{\left(n\right)}\right)^{2} \operatorname{im}{\left(n\right)} - \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(4 \left(\operatorname{re}{\left(n\right)}\right)^{3} \operatorname{im}{\left(n\right)} - 4 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{3}\right) - 4 \pi^{2} \left(5 \left(\operatorname{re}{\left(n\right)}\right)^{4} \operatorname{im}{\left(n\right)} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{3} + \left(\operatorname{im}{\left(n\right)}\right)^{5}\right),- \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{3} - 3 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{2}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(n\right)}\right)^{2} \left(\operatorname{im}{\left(n\right)}\right)^{2} + \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) - 4 \pi^{2} \left(\left(\operatorname{re}{\left(n\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(n\right)}\right)^{3} \left(\operatorname{im}{\left(n\right)}\right)^{2} + 5 \operatorname{re}{\left(n\right)} \left(\operatorname{im}{\left(n\right)}\right)^{4}\right) + 4 \right)}}{2} \right)} \operatorname{im}{\left(n\right)}}{\pi \left(\left(2 \operatorname{re}{\left(n\right)} + 1\right)^{2} + 4 \left(\operatorname{im}{\left(n\right)}\right)^{2}\right)}$$
x2 = (((-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5))^2 + (-pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)^2)^(1/4)*cos(atan2(-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5, -pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)/2) + 2)*(2*re(n) + 1)/(pi*((2*re(n) + 1)^2 + 4*im(n)^2)) + i*(-2*(((-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5))^2 + (-pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)^2)^(1/4)*cos(atan2(-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5), -pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)/2) + 2)*im(n)/(pi*((2*re(n) + 1)^2 + 4*im(n)^2)) + ((-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5))^2 + (-pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)^2)^(1/4)*(2*re(n) + 1)*sin(atan2(-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5), -pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)/2)/(pi*((2*re(n) + 1)^2 + 4*im(n)^2))) + 2*((-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5))^2 + (-pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)^2)^(1/4)*sin(atan2(-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5), -pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)/2)*im(n)/(pi*((2*re(n) + 1)^2 + 4*im(n)^2)))