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2*x^2-16*x-x*y+5*y=-34 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2*x - 16*x - x*y + 5*y = -34
$$5 y + \left(- x y + \left(2 x^{2} - 16 x\right)\right) = -34$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$5 y + \left(- x y + \left(2 x^{2} - 16 x\right)\right) = -34$$
en
$$\left(5 y + \left(- x y + \left(2 x^{2} - 16 x\right)\right)\right) + 34 = 0$$
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
$$a = 2$$
$$b = - y - 16$$
$$c = 5 y + 34$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{y}{4} + \frac{\sqrt{- 40 y + \left(- y - 16\right)^{2} - 272}}{4} + 4$$
$$x_{2} = \frac{y}{4} - \frac{\sqrt{- 40 y + \left(- y - 16\right)^{2} - 272}}{4} + 4$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$5 y + \left(- x y + \left(2 x^{2} - 16 x\right)\right) = -34$$
en
$$\left(5 y + \left(- x y + \left(2 x^{2} - 16 x\right)\right)\right) + 34 = 0$$
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
$$a = 2$$
$$b = - y - 16$$
$$c = 5 y + 34$$
, entonces
D = b^2 - 4 * a * c =
(-16 - y)^2 - 4 * (2) * (34 + 5*y) = -272 + (-16 - y)^2 - 40*y
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{y}{4} + \frac{\sqrt{- 40 y + \left(- y - 16\right)^{2} - 272}}{4} + 4$$
$$x_{2} = \frac{y}{4} - \frac{\sqrt{- 40 y + \left(- y - 16\right)^{2} - 272}}{4} + 4$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$5 y + \left(- x y + \left(2 x^{2} - 16 x\right)\right) = -34$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{x y}{2} - 8 x + \frac{5 y}{2} + 17 = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{y}{2} - 8$$
$$q = \frac{c}{a}$$
$$q = \frac{5 y}{2} + 17$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{y}{2} + 8$$
$$x_{1} x_{2} = \frac{5 y}{2} + 17$$
$$5 y + \left(- x y + \left(2 x^{2} - 16 x\right)\right) = -34$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{x y}{2} - 8 x + \frac{5 y}{2} + 17 = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{y}{2} - 8$$
$$q = \frac{c}{a}$$
$$q = \frac{5 y}{2} + 17$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{y}{2} + 8$$
$$x_{1} x_{2} = \frac{5 y}{2} + 17$$
Gráfica
Respuesta rápida
[src]
/ __________________________________________________________________ \ __________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-8*im(y) + 2*im(y)*re(y), -16 + re (y) - im (y) - 8*re(y)/|| 4 / 2 / 2 2 \ |atan2\-8*im(y) + 2*im(y)*re(y), -16 + re (y) - im (y) - 8*re(y)/|
| \/ (-8*im(y) + 2*im(y)*re(y)) + \-16 + re (y) - im (y) - 8*re(y)/ *sin|----------------------------------------------------------------|| \/ (-8*im(y) + 2*im(y)*re(y)) + \-16 + re (y) - im (y) - 8*re(y)/ *cos|----------------------------------------------------------------|
re(y) |im(y) \ 2 /| \ 2 /
x1 = 4 + ----- + I*|----- - --------------------------------------------------------------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------------------------------------------------------------------
4 \ 4 4 / 4
$$x_{1} = i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{4} + \frac{\operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{4} + \frac{\operatorname{re}{\left(y\right)}}{4} + 4$$
/ __________________________________________________________________ \ __________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-8*im(y) + 2*im(y)*re(y), -16 + re (y) - im (y) - 8*re(y)/|| 4 / 2 / 2 2 \ |atan2\-8*im(y) + 2*im(y)*re(y), -16 + re (y) - im (y) - 8*re(y)/|
| \/ (-8*im(y) + 2*im(y)*re(y)) + \-16 + re (y) - im (y) - 8*re(y)/ *sin|----------------------------------------------------------------|| \/ (-8*im(y) + 2*im(y)*re(y)) + \-16 + re (y) - im (y) - 8*re(y)/ *cos|----------------------------------------------------------------|
re(y) |im(y) \ 2 /| \ 2 /
x2 = 4 + ----- + I*|----- + --------------------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------
4 \ 4 4 / 4
$$x_{2} = i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{4} + \frac{\operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{4} + \frac{\operatorname{re}{\left(y\right)}}{4} + 4$$
x2 = i*(((2*re(y)*im(y) - 8*im(y))^2 + (re(y)^2 - 8*re(y) - im(y)^2 - 16)^2)^(1/4)*sin(atan2(2*re(y)*im(y) - 8*im(y, re(y)^2 - 8*re(y) - im(y)^2 - 16)/2)/4 + im(y)/4) + ((2*re(y)*im(y) - 8*im(y))^2 + (re(y)^2 - 8*re(y) - im(y)^2 - 16)^2)^(1/4)*cos(atan2(2*re(y)*im(y) - 8*im(y), re(y)^2 - 8*re(y) - im(y)^2 - 16)/2)/4 + re(y)/4 + 4)
Suma y producto de raíces
[src]
suma
/ __________________________________________________________________ \ __________________________________________________________________ / __________________________________________________________________ \ __________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\ | / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-8*im(y) + 2*im(y)*re(y), -16 + re (y) - im (y) - 8*re(y)/|| 4 / 2 / 2 2 \ |atan2\-8*im(y) + 2*im(y)*re(y), -16 + re (y) - im (y) - 8*re(y)/| | 4 / 2 / 2 2 \ |atan2\-8*im(y) + 2*im(y)*re(y), -16 + re (y) - im (y) - 8*re(y)/|| 4 / 2 / 2 2 \ |atan2\-8*im(y) + 2*im(y)*re(y), -16 + re (y) - im (y) - 8*re(y)/|
| \/ (-8*im(y) + 2*im(y)*re(y)) + \-16 + re (y) - im (y) - 8*re(y)/ *sin|----------------------------------------------------------------|| \/ (-8*im(y) + 2*im(y)*re(y)) + \-16 + re (y) - im (y) - 8*re(y)/ *cos|----------------------------------------------------------------| | \/ (-8*im(y) + 2*im(y)*re(y)) + \-16 + re (y) - im (y) - 8*re(y)/ *sin|----------------------------------------------------------------|| \/ (-8*im(y) + 2*im(y)*re(y)) + \-16 + re (y) - im (y) - 8*re(y)/ *cos|----------------------------------------------------------------|
re(y) |im(y) \ 2 /| \ 2 / re(y) |im(y) \ 2 /| \ 2 /
4 + ----- + I*|----- - --------------------------------------------------------------------------------------------------------------------------------------------| - -------------------------------------------------------------------------------------------------------------------------------------------- + 4 + ----- + I*|----- + --------------------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------
4 \ 4 4 / 4 4 \ 4 4 / 4
$$\left(i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{4} + \frac{\operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{4} + \frac{\operatorname{re}{\left(y\right)}}{4} + 4\right) + \left(i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{4} + \frac{\operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{4} + \frac{\operatorname{re}{\left(y\right)}}{4} + 4\right)$$
=
/ __________________________________________________________________ \ / __________________________________________________________________ \
| / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
| 4 / 2 / 2 2 \ |atan2\-8*im(y) + 2*im(y)*re(y), -16 + re (y) - im (y) - 8*re(y)/|| | 4 / 2 / 2 2 \ |atan2\-8*im(y) + 2*im(y)*re(y), -16 + re (y) - im (y) - 8*re(y)/||
| \/ (-8*im(y) + 2*im(y)*re(y)) + \-16 + re (y) - im (y) - 8*re(y)/ *sin|----------------------------------------------------------------|| | \/ (-8*im(y) + 2*im(y)*re(y)) + \-16 + re (y) - im (y) - 8*re(y)/ *sin|----------------------------------------------------------------||
re(y) |im(y) \ 2 /| |im(y) \ 2 /|
8 + ----- + I*|----- - --------------------------------------------------------------------------------------------------------------------------------------------| + I*|----- + --------------------------------------------------------------------------------------------------------------------------------------------|
2 \ 4 4 / \ 4 4 /
$$i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{4} + \frac{\operatorname{im}{\left(y\right)}}{4}\right) + i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{4} + \frac{\operatorname{im}{\left(y\right)}}{4}\right) + \frac{\operatorname{re}{\left(y\right)}}{2} + 8$$
producto
/ / __________________________________________________________________ \ __________________________________________________________________ \ / / __________________________________________________________________ \ __________________________________________________________________ \ | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | 4 / 2 / 2 2 \ |atan2\-8*im(y) + 2*im(y)*re(y), -16 + re (y) - im (y) - 8*re(y)/|| 4 / 2 / 2 2 \ |atan2\-8*im(y) + 2*im(y)*re(y), -16 + re (y) - im (y) - 8*re(y)/|| | | 4 / 2 / 2 2 \ |atan2\-8*im(y) + 2*im(y)*re(y), -16 + re (y) - im (y) - 8*re(y)/|| 4 / 2 / 2 2 \ |atan2\-8*im(y) + 2*im(y)*re(y), -16 + re (y) - im (y) - 8*re(y)/|| | | \/ (-8*im(y) + 2*im(y)*re(y)) + \-16 + re (y) - im (y) - 8*re(y)/ *sin|----------------------------------------------------------------|| \/ (-8*im(y) + 2*im(y)*re(y)) + \-16 + re (y) - im (y) - 8*re(y)/ *cos|----------------------------------------------------------------|| | | \/ (-8*im(y) + 2*im(y)*re(y)) + \-16 + re (y) - im (y) - 8*re(y)/ *sin|----------------------------------------------------------------|| \/ (-8*im(y) + 2*im(y)*re(y)) + \-16 + re (y) - im (y) - 8*re(y)/ *cos|----------------------------------------------------------------|| | re(y) |im(y) \ 2 /| \ 2 /| | re(y) |im(y) \ 2 /| \ 2 /| |4 + ----- + I*|----- - --------------------------------------------------------------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------------------------------------------------------------------|*|4 + ----- + I*|----- + --------------------------------------------------------------------------------------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------| \ 4 \ 4 4 / 4 / \ 4 \ 4 4 / 4 /
$$\left(i \left(- \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{4} + \frac{\operatorname{im}{\left(y\right)}}{4}\right) - \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{4} + \frac{\operatorname{re}{\left(y\right)}}{4} + 4\right) \left(i \left(\frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{4} + \frac{\operatorname{im}{\left(y\right)}}{4}\right) + \frac{\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 8 \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 16 \right)}}{2} \right)}}{4} + \frac{\operatorname{re}{\left(y\right)}}{4} + 4\right)$$
=
5*re(y) 5*I*im(y)
17 + ------- + ---------
2 2
$$\frac{5 \operatorname{re}{\left(y\right)}}{2} + \frac{5 i \operatorname{im}{\left(y\right)}}{2} + 17$$
17 + 5*re(y)/2 + 5*i*im(y)/2