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2*x^2-4x+2y^2+8y+10-a=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 2*x - 4*x + 2*y + 8*y + 10 - a = 0
$$- a + \left(\left(8 y + \left(2 y^{2} + \left(2 x^{2} - 4 x\right)\right)\right) + 10\right) = 0$$
Solución detallada
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
$$a = 2$$
$$b = -4$$
$$c = - a + 2 y^{2} + 8 y + 10$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{\sqrt{8 a - 16 y^{2} - 64 y - 64}}{4} + 1$$
$$x_{2} = 1 - \frac{\sqrt{8 a - 16 y^{2} - 64 y - 64}}{4}$$
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
$$a = 2$$
$$b = -4$$
$$c = - a + 2 y^{2} + 8 y + 10$$
, entonces
D = b^2 - 4 * a * c =
(-4)^2 - 4 * (2) * (10 - a + 2*y^2 + 8*y) = -64 - 64*y - 16*y^2 + 8*a
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{\sqrt{8 a - 16 y^{2} - 64 y - 64}}{4} + 1$$
$$x_{2} = 1 - \frac{\sqrt{8 a - 16 y^{2} - 64 y - 64}}{4}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$- a + \left(\left(8 y + \left(2 y^{2} + \left(2 x^{2} - 4 x\right)\right)\right) + 10\right) = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$- \frac{a}{2} + x^{2} - 2 x + y^{2} + 4 y + 5 = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = - \frac{a}{2} + y^{2} + 4 y + 5$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = - \frac{a}{2} + y^{2} + 4 y + 5$$
$$- a + \left(\left(8 y + \left(2 y^{2} + \left(2 x^{2} - 4 x\right)\right)\right) + 10\right) = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$- \frac{a}{2} + x^{2} - 2 x + y^{2} + 4 y + 5 = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = - \frac{a}{2} + y^{2} + 4 y + 5$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = - \frac{a}{2} + y^{2} + 4 y + 5$$
Gráfica
Respuesta rápida
[src]
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / 2 / 2 2 \ |atan2\-16*im(y) + 2*im(a) - 8*im(y)*re(y), -16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/| 4 / 2 / 2 2 \ |atan2\-16*im(y) + 2*im(a) - 8*im(y)*re(y), -16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/|
\/ (-16*im(y) + 2*im(a) - 8*im(y)*re(y)) + \-16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/ *cos|------------------------------------------------------------------------------------------| I*\/ (-16*im(y) + 2*im(a) - 8*im(y)*re(y)) + \-16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/ *sin|------------------------------------------------------------------------------------------|
\ 2 / \ 2 /
x1 = 1 - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{1} = - \frac{i \sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{2} - \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{2} + 1$$
____________________________________________________________________________________________ ____________________________________________________________________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / 2 / 2 2 \ |atan2\-16*im(y) + 2*im(a) - 8*im(y)*re(y), -16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/| 4 / 2 / 2 2 \ |atan2\-16*im(y) + 2*im(a) - 8*im(y)*re(y), -16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/|
\/ (-16*im(y) + 2*im(a) - 8*im(y)*re(y)) + \-16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/ *cos|------------------------------------------------------------------------------------------| I*\/ (-16*im(y) + 2*im(a) - 8*im(y)*re(y)) + \-16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/ *sin|------------------------------------------------------------------------------------------|
\ 2 / \ 2 /
x2 = 1 + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{2} = \frac{i \sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{2} + \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{2} + 1$$
x2 = i*((-8*re(y)*im(y) + 2*im(a) - 16*im(y))^2 + (2*re(a) - 4*re(y)^2 - 16*re(y) + 4*im(y)^2 - 16)^2)^(1/4)*sin(atan2(-8*re(y)*im(y) + 2*im(a) - 16*im(y, 2*re(a) - 4*re(y)^2 - 16*re(y) + 4*im(y)^2 - 16)/2)/2 + ((-8*re(y)*im(y) + 2*im(a) - 16*im(y))^2 + (2*re(a) - 4*re(y)^2 - 16*re(y) + 4*im(y)^2 - 16)^2)^(1/4)*cos(atan2(-8*re(y)*im(y) + 2*im(a) - 16*im(y), 2*re(a) - 4*re(y)^2 - 16*re(y) + 4*im(y)^2 - 16)/2)/2 + 1)
Suma y producto de raíces
[src]
suma
____________________________________________________________________________________________ ____________________________________________________________________________________________ ____________________________________________________________________________________________ ____________________________________________________________________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / 2 / 2 2 \ |atan2\-16*im(y) + 2*im(a) - 8*im(y)*re(y), -16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/| 4 / 2 / 2 2 \ |atan2\-16*im(y) + 2*im(a) - 8*im(y)*re(y), -16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/| 4 / 2 / 2 2 \ |atan2\-16*im(y) + 2*im(a) - 8*im(y)*re(y), -16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/| 4 / 2 / 2 2 \ |atan2\-16*im(y) + 2*im(a) - 8*im(y)*re(y), -16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/|
\/ (-16*im(y) + 2*im(a) - 8*im(y)*re(y)) + \-16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/ *cos|------------------------------------------------------------------------------------------| I*\/ (-16*im(y) + 2*im(a) - 8*im(y)*re(y)) + \-16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/ *sin|------------------------------------------------------------------------------------------| \/ (-16*im(y) + 2*im(a) - 8*im(y)*re(y)) + \-16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/ *cos|------------------------------------------------------------------------------------------| I*\/ (-16*im(y) + 2*im(a) - 8*im(y)*re(y)) + \-16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/ *sin|------------------------------------------------------------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
1 - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 1 + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2 2 2
$$\left(- \frac{i \sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{2} - \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{2} + 1\right) + \left(\frac{i \sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{2} + \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{2} + 1\right)$$
=
2
$$2$$
producto
/ ____________________________________________________________________________________________ ____________________________________________________________________________________________ \ / ____________________________________________________________________________________________ ____________________________________________________________________________________________ \ | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | 4 / 2 / 2 2 \ |atan2\-16*im(y) + 2*im(a) - 8*im(y)*re(y), -16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/| 4 / 2 / 2 2 \ |atan2\-16*im(y) + 2*im(a) - 8*im(y)*re(y), -16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/|| | 4 / 2 / 2 2 \ |atan2\-16*im(y) + 2*im(a) - 8*im(y)*re(y), -16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/| 4 / 2 / 2 2 \ |atan2\-16*im(y) + 2*im(a) - 8*im(y)*re(y), -16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/|| | \/ (-16*im(y) + 2*im(a) - 8*im(y)*re(y)) + \-16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/ *cos|------------------------------------------------------------------------------------------| I*\/ (-16*im(y) + 2*im(a) - 8*im(y)*re(y)) + \-16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/ *sin|------------------------------------------------------------------------------------------|| | \/ (-16*im(y) + 2*im(a) - 8*im(y)*re(y)) + \-16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/ *cos|------------------------------------------------------------------------------------------| I*\/ (-16*im(y) + 2*im(a) - 8*im(y)*re(y)) + \-16 - 16*re(y) - 4*re (y) + 2*re(a) + 4*im (y)/ *sin|------------------------------------------------------------------------------------------|| | \ 2 / \ 2 /| | \ 2 / \ 2 /| |1 - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|1 + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 2 2 / \ 2 2 /
$$\left(- \frac{i \sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{2} - \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{2} + 1\right) \left(\frac{i \sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{2} + \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} - 16 \operatorname{im}{\left(y\right)},2 \operatorname{re}{\left(a\right)} - 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 16 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{2} + 1\right)$$
=
2 2 re(a) I*im(a)
5 + re (y) - im (y) + 4*re(y) - ----- + 4*I*im(y) - ------- + 2*I*im(y)*re(y)
2 2
$$- \frac{\operatorname{re}{\left(a\right)}}{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + 2 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 4 \operatorname{re}{\left(y\right)} - \frac{i \operatorname{im}{\left(a\right)}}{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4 i \operatorname{im}{\left(y\right)} + 5$$
5 + re(y)^2 - im(y)^2 + 4*re(y) - re(a)/2 + 4*i*im(y) - i*im(a)/2 + 2*i*im(y)*re(y)