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- La ecuación:
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Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
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Ecuación x^2-14*x+33=0
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Ecuación x+18=8
- Expresar {x} en función de y en la ecuación:
- 12*x+1*y=15
- -17*x-12*y=-9
- 18*x+17*y=-14
- 16*x-17*y=-15
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Expresiones idénticas
- nueve *((x- dos)^ dos +(y+ cuatro)^ dos)= cuatro *((x- dos)^ dos +(y- cinco)^ dos)
- 9 multiplicar por ((x menos 2) al cuadrado más (y más 4) al cuadrado ) es igual a 4 multiplicar por ((x menos 2) al cuadrado más (y menos 5) al cuadrado )
- nueve multiplicar por ((x menos dos) en el grado dos más (y más cuatro) en el grado dos) es igual a cuatro multiplicar por ((x menos dos) en el grado dos más (y menos cinco) en el grado dos)
- 9*((x-2)2+(y+4)2)=4*((x-2)2+(y-5)2)
- 9*x-22+y+42=4*x-22+y-52
- 9*((x-2)²+(y+4)²)=4*((x-2)²+(y-5)²)
- 9*((x-2) en el grado 2+(y+4) en el grado 2)=4*((x-2) en el grado 2+(y-5) en el grado 2)
- 9((x-2)^2+(y+4)^2)=4((x-2)^2+(y-5)^2)
- 9((x-2)2+(y+4)2)=4((x-2)2+(y-5)2)
- 9x-22+y+42=4x-22+y-52
- 9x-2^2+y+4^2=4x-2^2+y-5^2
-
Expresiones semejantes
- 9*((x-2)^2-(y+4)^2)=4*((x-2)^2+(y-5)^2)
- 9*((x+2)^2+(y+4)^2)=4*((x-2)^2+(y-5)^2)
- 9*((x-2)^2+(y+4)^2)=4*((x+2)^2+(y-5)^2)
- 9*((x-2)^2+(y+4)^2)=4*((x-2)^2+(y+5)^2)
- 9*((x-2)^2+(y+4)^2)=4*((x-2)^2-(y-5)^2)
- 9*((x-2)^2+(y-4)^2)=4*((x-2)^2+(y-5)^2)
9*((x-2)^2+(y+4)^2)=4*((x-2)^2+(y-5)^2) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 2 2\ / 2 2\ 9*\(x - 2) + (y + 4) / = 4*\(x - 2) + (y - 5) /
$$9 \left(\left(x - 2\right)^{2} + \left(y + 4\right)^{2}\right) = 4 \left(\left(x - 2\right)^{2} + \left(y - 5\right)^{2}\right)$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$9 \left(\left(x - 2\right)^{2} + \left(y + 4\right)^{2}\right) = 4 \left(\left(x - 2\right)^{2} + \left(y - 5\right)^{2}\right)$$
en
$$- 4 \left(\left(x - 2\right)^{2} + \left(y - 5\right)^{2}\right) + 9 \left(\left(x - 2\right)^{2} + \left(y + 4\right)^{2}\right) = 0$$
Abramos la expresión en la ecuación
$$- 4 \left(\left(x - 2\right)^{2} + \left(y - 5\right)^{2}\right) + 9 \left(\left(x - 2\right)^{2} + \left(y + 4\right)^{2}\right) = 0$$
Obtenemos la ecuación cuadrática
$$5 x^{2} - 20 x + 5 y^{2} + 112 y + 64 = 0$$
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
$$a = 5$$
$$b = -20$$
$$c = 5 y^{2} + 112 y + 64$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{\sqrt{- 100 y^{2} - 2240 y - 880}}{10} + 2$$
$$x_{2} = 2 - \frac{\sqrt{- 100 y^{2} - 2240 y - 880}}{10}$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$9 \left(\left(x - 2\right)^{2} + \left(y + 4\right)^{2}\right) = 4 \left(\left(x - 2\right)^{2} + \left(y - 5\right)^{2}\right)$$
en
$$- 4 \left(\left(x - 2\right)^{2} + \left(y - 5\right)^{2}\right) + 9 \left(\left(x - 2\right)^{2} + \left(y + 4\right)^{2}\right) = 0$$
Abramos la expresión en la ecuación
$$- 4 \left(\left(x - 2\right)^{2} + \left(y - 5\right)^{2}\right) + 9 \left(\left(x - 2\right)^{2} + \left(y + 4\right)^{2}\right) = 0$$
Obtenemos la ecuación cuadrática
$$5 x^{2} - 20 x + 5 y^{2} + 112 y + 64 = 0$$
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
$$a = 5$$
$$b = -20$$
$$c = 5 y^{2} + 112 y + 64$$
, entonces
D = b^2 - 4 * a * c =
(-20)^2 - 4 * (5) * (64 + 5*y^2 + 112*y) = -880 - 2240*y - 100*y^2
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{\sqrt{- 100 y^{2} - 2240 y - 880}}{10} + 2$$
$$x_{2} = 2 - \frac{\sqrt{- 100 y^{2} - 2240 y - 880}}{10}$$
Gráfica
Respuesta rápida
[src]
______________________________________________________________________________ ______________________________________________________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / 2 / 2 2 \ |atan2\-560*im(y) - 50*im(y)*re(y), -220 - 560*re(y) - 25*re (y) + 25*im (y)/| 4 / 2 / 2 2 \ |atan2\-560*im(y) - 50*im(y)*re(y), -220 - 560*re(y) - 25*re (y) + 25*im (y)/|
\/ (-560*im(y) - 50*im(y)*re(y)) + \-220 - 560*re(y) - 25*re (y) + 25*im (y)/ *cos|----------------------------------------------------------------------------| I*\/ (-560*im(y) - 50*im(y)*re(y)) + \-220 - 560*re(y) - 25*re (y) + 25*im (y)/ *sin|----------------------------------------------------------------------------|
\ 2 / \ 2 /
x1 = 2 - -------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------
5 5
$$x_{1} = - \frac{i \sqrt[4]{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)},- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220 \right)}}{2} \right)}}{5} - \frac{\sqrt[4]{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)},- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220 \right)}}{2} \right)}}{5} + 2$$
______________________________________________________________________________ ______________________________________________________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / 2 / 2 2 \ |atan2\-560*im(y) - 50*im(y)*re(y), -220 - 560*re(y) - 25*re (y) + 25*im (y)/| 4 / 2 / 2 2 \ |atan2\-560*im(y) - 50*im(y)*re(y), -220 - 560*re(y) - 25*re (y) + 25*im (y)/|
\/ (-560*im(y) - 50*im(y)*re(y)) + \-220 - 560*re(y) - 25*re (y) + 25*im (y)/ *cos|----------------------------------------------------------------------------| I*\/ (-560*im(y) - 50*im(y)*re(y)) + \-220 - 560*re(y) - 25*re (y) + 25*im (y)/ *sin|----------------------------------------------------------------------------|
\ 2 / \ 2 /
x2 = 2 + -------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------
5 5
$$x_{2} = \frac{i \sqrt[4]{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)},- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220 \right)}}{2} \right)}}{5} + \frac{\sqrt[4]{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)},- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220 \right)}}{2} \right)}}{5} + 2$$
x2 = i*((-50*re(y)*im(y) - 560*im(y))^2 + (-25*re(y)^2 - 560*re(y) + 25*im(y)^2 - 220)^2)^(1/4)*sin(atan2(-50*re(y)*im(y) - 560*im(y, -25*re(y)^2 - 560*re(y) + 25*im(y)^2 - 220)/2)/5 + ((-50*re(y)*im(y) - 560*im(y))^2 + (-25*re(y)^2 - 560*re(y) + 25*im(y)^2 - 220)^2)^(1/4)*cos(atan2(-50*re(y)*im(y) - 560*im(y), -25*re(y)^2 - 560*re(y) + 25*im(y)^2 - 220)/2)/5 + 2)
Suma y producto de raíces
[src]
suma
______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / 2 / 2 2 \ |atan2\-560*im(y) - 50*im(y)*re(y), -220 - 560*re(y) - 25*re (y) + 25*im (y)/| 4 / 2 / 2 2 \ |atan2\-560*im(y) - 50*im(y)*re(y), -220 - 560*re(y) - 25*re (y) + 25*im (y)/| 4 / 2 / 2 2 \ |atan2\-560*im(y) - 50*im(y)*re(y), -220 - 560*re(y) - 25*re (y) + 25*im (y)/| 4 / 2 / 2 2 \ |atan2\-560*im(y) - 50*im(y)*re(y), -220 - 560*re(y) - 25*re (y) + 25*im (y)/|
\/ (-560*im(y) - 50*im(y)*re(y)) + \-220 - 560*re(y) - 25*re (y) + 25*im (y)/ *cos|----------------------------------------------------------------------------| I*\/ (-560*im(y) - 50*im(y)*re(y)) + \-220 - 560*re(y) - 25*re (y) + 25*im (y)/ *sin|----------------------------------------------------------------------------| \/ (-560*im(y) - 50*im(y)*re(y)) + \-220 - 560*re(y) - 25*re (y) + 25*im (y)/ *cos|----------------------------------------------------------------------------| I*\/ (-560*im(y) - 50*im(y)*re(y)) + \-220 - 560*re(y) - 25*re (y) + 25*im (y)/ *sin|----------------------------------------------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
2 - -------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 2 + -------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------
5 5 5 5
$$\left(- \frac{i \sqrt[4]{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)},- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220 \right)}}{2} \right)}}{5} - \frac{\sqrt[4]{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)},- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220 \right)}}{2} \right)}}{5} + 2\right) + \left(\frac{i \sqrt[4]{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)},- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220 \right)}}{2} \right)}}{5} + \frac{\sqrt[4]{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)},- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220 \right)}}{2} \right)}}{5} + 2\right)$$
=
4
$$4$$
producto
/ ______________________________________________________________________________ ______________________________________________________________________________ \ / ______________________________________________________________________________ ______________________________________________________________________________ \ | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | 4 / 2 / 2 2 \ |atan2\-560*im(y) - 50*im(y)*re(y), -220 - 560*re(y) - 25*re (y) + 25*im (y)/| 4 / 2 / 2 2 \ |atan2\-560*im(y) - 50*im(y)*re(y), -220 - 560*re(y) - 25*re (y) + 25*im (y)/|| | 4 / 2 / 2 2 \ |atan2\-560*im(y) - 50*im(y)*re(y), -220 - 560*re(y) - 25*re (y) + 25*im (y)/| 4 / 2 / 2 2 \ |atan2\-560*im(y) - 50*im(y)*re(y), -220 - 560*re(y) - 25*re (y) + 25*im (y)/|| | \/ (-560*im(y) - 50*im(y)*re(y)) + \-220 - 560*re(y) - 25*re (y) + 25*im (y)/ *cos|----------------------------------------------------------------------------| I*\/ (-560*im(y) - 50*im(y)*re(y)) + \-220 - 560*re(y) - 25*re (y) + 25*im (y)/ *sin|----------------------------------------------------------------------------|| | \/ (-560*im(y) - 50*im(y)*re(y)) + \-220 - 560*re(y) - 25*re (y) + 25*im (y)/ *cos|----------------------------------------------------------------------------| I*\/ (-560*im(y) - 50*im(y)*re(y)) + \-220 - 560*re(y) - 25*re (y) + 25*im (y)/ *sin|----------------------------------------------------------------------------|| | \ 2 / \ 2 /| | \ 2 / \ 2 /| |2 - -------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|2 + -------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 5 5 / \ 5 5 /
$$\left(- \frac{i \sqrt[4]{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)},- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220 \right)}}{2} \right)}}{5} - \frac{\sqrt[4]{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)},- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220 \right)}}{2} \right)}}{5} + 2\right) \left(\frac{i \sqrt[4]{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)},- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220 \right)}}{2} \right)}}{5} + \frac{\sqrt[4]{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 50 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 560 \operatorname{im}{\left(y\right)},- 25 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 560 \operatorname{re}{\left(y\right)} + 25 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 220 \right)}}{2} \right)}}{5} + 2\right)$$
=
64 2 2 112*re(y) 112*I*im(y) -- + re (y) - im (y) + --------- + ----------- + 2*I*im(y)*re(y) 5 5 5
$$\left(\operatorname{re}{\left(y\right)}\right)^{2} + 2 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \frac{112 \operatorname{re}{\left(y\right)}}{5} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + \frac{112 i \operatorname{im}{\left(y\right)}}{5} + \frac{64}{5}$$
64/5 + re(y)^2 - im(y)^2 + 112*re(y)/5 + 112*i*im(y)/5 + 2*i*im(y)*re(y)