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- -18*x-2*y=9
- -14*x+10*y=19
- -9*x+1*y=3
- -17*x+1*y=-11
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Expresiones idénticas
- (ciento sesenta *x-x^ dos)+((ciento sesenta *y-y^ dos)/ dos)= diez +(uno / dos)*(x+y)
- (160 multiplicar por x menos x al cuadrado ) más ((160 multiplicar por y menos y al cuadrado ) dividir por 2) es igual a 10 más (1 dividir por 2) multiplicar por (x más y)
- (ciento sesenta multiplicar por x menos x en el grado dos) más ((ciento sesenta multiplicar por y menos y en el grado dos) dividir por dos) es igual a diez más (uno dividir por dos) multiplicar por (x más y)
- (160*x-x2)+((160*y-y2)/2)=10+(1/2)*(x+y)
- 160*x-x2+160*y-y2/2=10+1/2*x+y
- (160*x-x²)+((160*y-y²)/2)=10+(1/2)*(x+y)
- (160*x-x en el grado 2)+((160*y-y en el grado 2)/2)=10+(1/2)*(x+y)
- (160x-x^2)+((160y-y^2)/2)=10+(1/2)(x+y)
- (160x-x2)+((160y-y2)/2)=10+(1/2)(x+y)
- 160x-x2+160y-y2/2=10+1/2x+y
- 160x-x^2+160y-y^2/2=10+1/2x+y
- (160*x-x^2)+((160*y-y^2) dividir por 2)=10+(1 dividir por 2)*(x+y)
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Expresiones semejantes
- (160*x-x^2)+((160*y-y^2)/2)=10-(1/2)*(x+y)
- (160*x+x^2)+((160*y-y^2)/2)=10+(1/2)*(x+y)
- (160*x-x^2)+((160*y-y^2)/2)=10+(1/2)*(x-y)
- (160*x-x^2)+((160*y+y^2)/2)=10+(1/2)*(x+y)
- (160*x-x^2)-((160*y-y^2)/2)=10+(1/2)*(x+y)
(160*x-x^2)+((160*y-y^2)/2)=10+(1/2)*(x+y) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2
2 160*y - y x + y
160*x - x + ---------- = 10 + -----
2 2
$$\left(- x^{2} + 160 x\right) + \frac{- y^{2} + 160 y}{2} = \frac{x + y}{2} + 10$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$\left(- x^{2} + 160 x\right) + \frac{- y^{2} + 160 y}{2} = \frac{x + y}{2} + 10$$
en
$$\left(- \frac{x + y}{2} - 10\right) + \left(\left(- x^{2} + 160 x\right) + \frac{- y^{2} + 160 y}{2}\right) = 0$$
Abramos la expresión en la ecuación
$$\left(- \frac{x + y}{2} - 10\right) + \left(\left(- x^{2} + 160 x\right) + \frac{- y^{2} + 160 y}{2}\right) = 0$$
Obtenemos la ecuación cuadrática
$$- x^{2} + \frac{319 x}{2} - \frac{y^{2}}{2} + \frac{159 y}{2} - 10 = 0$$
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
$$a = -1$$
$$b = \frac{319}{2}$$
$$c = - \frac{y^{2}}{2} + \frac{159 y}{2} - 10$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{319}{4} - \frac{\sqrt{- 2 y^{2} + 318 y + \frac{101601}{4}}}{2}$$
$$x_{2} = \frac{\sqrt{- 2 y^{2} + 318 y + \frac{101601}{4}}}{2} + \frac{319}{4}$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$\left(- x^{2} + 160 x\right) + \frac{- y^{2} + 160 y}{2} = \frac{x + y}{2} + 10$$
en
$$\left(- \frac{x + y}{2} - 10\right) + \left(\left(- x^{2} + 160 x\right) + \frac{- y^{2} + 160 y}{2}\right) = 0$$
Abramos la expresión en la ecuación
$$\left(- \frac{x + y}{2} - 10\right) + \left(\left(- x^{2} + 160 x\right) + \frac{- y^{2} + 160 y}{2}\right) = 0$$
Obtenemos la ecuación cuadrática
$$- x^{2} + \frac{319 x}{2} - \frac{y^{2}}{2} + \frac{159 y}{2} - 10 = 0$$
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
$$a = -1$$
$$b = \frac{319}{2}$$
$$c = - \frac{y^{2}}{2} + \frac{159 y}{2} - 10$$
, entonces
D = b^2 - 4 * a * c =
(319/2)^2 - 4 * (-1) * (-10 - y^2/2 + 159*y/2) = 101601/4 - 2*y^2 + 318*y
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{319}{4} - \frac{\sqrt{- 2 y^{2} + 318 y + \frac{101601}{4}}}{2}$$
$$x_{2} = \frac{\sqrt{- 2 y^{2} + 318 y + \frac{101601}{4}}}{2} + \frac{319}{4}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(- x^{2} + 160 x\right) + \frac{- y^{2} + 160 y}{2} = \frac{x + y}{2} + 10$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{319 x}{2} + \frac{y^{2}}{2} - \frac{159 y}{2} + 10 = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{319}{2}$$
$$q = \frac{c}{a}$$
$$q = \frac{y^{2}}{2} - \frac{159 y}{2} + 10$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{319}{2}$$
$$x_{1} x_{2} = \frac{y^{2}}{2} - \frac{159 y}{2} + 10$$
$$\left(- x^{2} + 160 x\right) + \frac{- y^{2} + 160 y}{2} = \frac{x + y}{2} + 10$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{319 x}{2} + \frac{y^{2}}{2} - \frac{159 y}{2} + 10 = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{319}{2}$$
$$q = \frac{c}{a}$$
$$q = \frac{y^{2}}{2} - \frac{159 y}{2} + 10$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{319}{2}$$
$$x_{1} x_{2} = \frac{y^{2}}{2} - \frac{159 y}{2} + 10$$
Gráfica
Respuesta rápida
[src]
_______________________________________________________________________________ _______________________________________________________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / 2 / 2 2 \ |atan2\1272*im(y) - 16*im(y)*re(y), 101601 - 8*re (y) + 8*im (y) + 1272*re(y)/| 4 / 2 / 2 2 \ |atan2\1272*im(y) - 16*im(y)*re(y), 101601 - 8*re (y) + 8*im (y) + 1272*re(y)/|
\/ (1272*im(y) - 16*im(y)*re(y)) + \101601 - 8*re (y) + 8*im (y) + 1272*re(y)/ *cos|-----------------------------------------------------------------------------| I*\/ (1272*im(y) - 16*im(y)*re(y)) + \101601 - 8*re (y) + 8*im (y) + 1272*re(y)/ *sin|-----------------------------------------------------------------------------|
319 \ 2 / \ 2 /
x1 = --- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4 4 4
$$x_{1} = - \frac{i \sqrt[4]{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601 \right)}}{2} \right)}}{4} - \frac{\sqrt[4]{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601 \right)}}{2} \right)}}{4} + \frac{319}{4}$$
_______________________________________________________________________________ _______________________________________________________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / 2 / 2 2 \ |atan2\1272*im(y) - 16*im(y)*re(y), 101601 - 8*re (y) + 8*im (y) + 1272*re(y)/| 4 / 2 / 2 2 \ |atan2\1272*im(y) - 16*im(y)*re(y), 101601 - 8*re (y) + 8*im (y) + 1272*re(y)/|
\/ (1272*im(y) - 16*im(y)*re(y)) + \101601 - 8*re (y) + 8*im (y) + 1272*re(y)/ *cos|-----------------------------------------------------------------------------| I*\/ (1272*im(y) - 16*im(y)*re(y)) + \101601 - 8*re (y) + 8*im (y) + 1272*re(y)/ *sin|-----------------------------------------------------------------------------|
319 \ 2 / \ 2 /
x2 = --- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4 4 4
$$x_{2} = \frac{i \sqrt[4]{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601 \right)}}{2} \right)}}{4} + \frac{\sqrt[4]{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601 \right)}}{2} \right)}}{4} + \frac{319}{4}$$
x2 = i*((-16*re(y)*im(y) + 1272*im(y))^2 + (-8*re(y)^2 + 1272*re(y) + 8*im(y)^2 + 101601)^2)^(1/4)*sin(atan2(-16*re(y)*im(y) + 1272*im(y, -8*re(y)^2 + 1272*re(y) + 8*im(y)^2 + 101601)/2)/4 + ((-16*re(y)*im(y) + 1272*im(y))^2 + (-8*re(y)^2 + 1272*re(y) + 8*im(y)^2 + 101601)^2)^(1/4)*cos(atan2(-16*re(y)*im(y) + 1272*im(y), -8*re(y)^2 + 1272*re(y) + 8*im(y)^2 + 101601)/2)/4 + 319/4)
Suma y producto de raíces
[src]
suma
_______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / 2 / 2 2 \ |atan2\1272*im(y) - 16*im(y)*re(y), 101601 - 8*re (y) + 8*im (y) + 1272*re(y)/| 4 / 2 / 2 2 \ |atan2\1272*im(y) - 16*im(y)*re(y), 101601 - 8*re (y) + 8*im (y) + 1272*re(y)/| 4 / 2 / 2 2 \ |atan2\1272*im(y) - 16*im(y)*re(y), 101601 - 8*re (y) + 8*im (y) + 1272*re(y)/| 4 / 2 / 2 2 \ |atan2\1272*im(y) - 16*im(y)*re(y), 101601 - 8*re (y) + 8*im (y) + 1272*re(y)/|
\/ (1272*im(y) - 16*im(y)*re(y)) + \101601 - 8*re (y) + 8*im (y) + 1272*re(y)/ *cos|-----------------------------------------------------------------------------| I*\/ (1272*im(y) - 16*im(y)*re(y)) + \101601 - 8*re (y) + 8*im (y) + 1272*re(y)/ *sin|-----------------------------------------------------------------------------| \/ (1272*im(y) - 16*im(y)*re(y)) + \101601 - 8*re (y) + 8*im (y) + 1272*re(y)/ *cos|-----------------------------------------------------------------------------| I*\/ (1272*im(y) - 16*im(y)*re(y)) + \101601 - 8*re (y) + 8*im (y) + 1272*re(y)/ *sin|-----------------------------------------------------------------------------|
319 \ 2 / \ 2 / 319 \ 2 / \ 2 /
--- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4 4 4 4 4 4
$$\left(- \frac{i \sqrt[4]{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601 \right)}}{2} \right)}}{4} - \frac{\sqrt[4]{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601 \right)}}{2} \right)}}{4} + \frac{319}{4}\right) + \left(\frac{i \sqrt[4]{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601 \right)}}{2} \right)}}{4} + \frac{\sqrt[4]{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601 \right)}}{2} \right)}}{4} + \frac{319}{4}\right)$$
=
319/2
$$\frac{319}{2}$$
producto
/ _______________________________________________________________________________ _______________________________________________________________________________ \ / _______________________________________________________________________________ _______________________________________________________________________________ \ | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | 4 / 2 / 2 2 \ |atan2\1272*im(y) - 16*im(y)*re(y), 101601 - 8*re (y) + 8*im (y) + 1272*re(y)/| 4 / 2 / 2 2 \ |atan2\1272*im(y) - 16*im(y)*re(y), 101601 - 8*re (y) + 8*im (y) + 1272*re(y)/|| | 4 / 2 / 2 2 \ |atan2\1272*im(y) - 16*im(y)*re(y), 101601 - 8*re (y) + 8*im (y) + 1272*re(y)/| 4 / 2 / 2 2 \ |atan2\1272*im(y) - 16*im(y)*re(y), 101601 - 8*re (y) + 8*im (y) + 1272*re(y)/|| | \/ (1272*im(y) - 16*im(y)*re(y)) + \101601 - 8*re (y) + 8*im (y) + 1272*re(y)/ *cos|-----------------------------------------------------------------------------| I*\/ (1272*im(y) - 16*im(y)*re(y)) + \101601 - 8*re (y) + 8*im (y) + 1272*re(y)/ *sin|-----------------------------------------------------------------------------|| | \/ (1272*im(y) - 16*im(y)*re(y)) + \101601 - 8*re (y) + 8*im (y) + 1272*re(y)/ *cos|-----------------------------------------------------------------------------| I*\/ (1272*im(y) - 16*im(y)*re(y)) + \101601 - 8*re (y) + 8*im (y) + 1272*re(y)/ *sin|-----------------------------------------------------------------------------|| |319 \ 2 / \ 2 /| |319 \ 2 / \ 2 /| |--- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|--- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 4 4 4 / \ 4 4 4 /
$$\left(- \frac{i \sqrt[4]{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601 \right)}}{2} \right)}}{4} - \frac{\sqrt[4]{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601 \right)}}{2} \right)}}{4} + \frac{319}{4}\right) \left(\frac{i \sqrt[4]{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601 \right)}}{2} \right)}}{4} + \frac{\sqrt[4]{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1272 \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 1272 \operatorname{re}{\left(y\right)} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 101601 \right)}}{2} \right)}}{4} + \frac{319}{4}\right)$$
=
2 2
re (y) 159*re(y) im (y) 159*I*im(y)
10 + ------ - --------- - ------ - ----------- + I*im(y)*re(y)
2 2 2 2
$$\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{2} + i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \frac{159 \operatorname{re}{\left(y\right)}}{2} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{2} - \frac{159 i \operatorname{im}{\left(y\right)}}{2} + 10$$
10 + re(y)^2/2 - 159*re(y)/2 - im(y)^2/2 - 159*i*im(y)/2 + i*im(y)*re(y)