Sr Examen
Otras calculadoras
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- La ecuación:
-
Ecuación 6*x^2+x-7=0
-
Ecuación 2-5(3+2x)=17
-
Ecuación (6*x+8)/2+5=5*x/3
-
Ecuación 10/(x+6)=1
- Expresar {x} en función de y en la ecuación:
- -9*x-12*y=-19
- -8*x+3*y=-4
- 10*x+3*y=2
- -10*x-12*y=-10
- Forma canónica:
- (x-2)^2+(y-3)^2
-
Expresiones idénticas
- (x- dos)^ dos +(y- tres)^ dos = nueve
- (x menos 2) al cuadrado más (y menos 3) al cuadrado es igual a 9
- (x menos dos) en el grado dos más (y menos tres) en el grado dos es igual a nueve
- (x-2)2+(y-3)2=9
- x-22+y-32=9
- (x-2)²+(y-3)²=9
- (x-2) en el grado 2+(y-3) en el grado 2=9
- x-2^2+y-3^2=9
-
Expresiones semejantes
- (x+2)^2+(y-3)^2=9
- (x-2)^2-(y-3)^2=9
- (x-2)^2+(y+3)^2=9
(x-2)^2+(y-3)^2=9 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 (x - 2) + (y - 3) = 9
$$\left(x - 2\right)^{2} + \left(y - 3\right)^{2} = 9$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$\left(x - 2\right)^{2} + \left(y - 3\right)^{2} = 9$$
en
$$\left(\left(x - 2\right)^{2} + \left(y - 3\right)^{2}\right) - 9 = 0$$
Abramos la expresión en la ecuación
$$\left(\left(x - 2\right)^{2} + \left(y - 3\right)^{2}\right) - 9 = 0$$
Obtenemos la ecuación cuadrática
$$x^{2} - 4 x + y^{2} - 6 y + 4 = 0$$
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
$$a = 1$$
$$b = -4$$
$$c = y^{2} - 6 y + 4$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{\sqrt{- 4 y^{2} + 24 y}}{2} + 2$$
$$x_{2} = 2 - \frac{\sqrt{- 4 y^{2} + 24 y}}{2}$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$\left(x - 2\right)^{2} + \left(y - 3\right)^{2} = 9$$
en
$$\left(\left(x - 2\right)^{2} + \left(y - 3\right)^{2}\right) - 9 = 0$$
Abramos la expresión en la ecuación
$$\left(\left(x - 2\right)^{2} + \left(y - 3\right)^{2}\right) - 9 = 0$$
Obtenemos la ecuación cuadrática
$$x^{2} - 4 x + y^{2} - 6 y + 4 = 0$$
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
$$a = 1$$
$$b = -4$$
$$c = y^{2} - 6 y + 4$$
, entonces
D = b^2 - 4 * a * c =
(-4)^2 - 4 * (1) * (4 + y^2 - 6*y) = -4*y^2 + 24*y
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{\sqrt{- 4 y^{2} + 24 y}}{2} + 2$$
$$x_{2} = 2 - \frac{\sqrt{- 4 y^{2} + 24 y}}{2}$$
Gráfica
Respuesta rápida
[src]
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/ 2 / / 2 \\ / 2 / / 2 \\
4 / / 2 \ 2 |atan2\-(-6 + re(y))*im(y) - im(y)*re(y), im (y) - (-6 + re(y))*re(y)/| 4 / / 2 \ 2 |atan2\-(-6 + re(y))*im(y) - im(y)*re(y), im (y) - (-6 + re(y))*re(y)/|
x1 = 2 - \/ \im (y) - (-6 + re(y))*re(y)/ + (-(-6 + re(y))*im(y) - im(y)*re(y)) *cos|---------------------------------------------------------------------| - I*\/ \im (y) - (-6 + re(y))*re(y)/ + (-(-6 + re(y))*im(y) - im(y)*re(y)) *sin|---------------------------------------------------------------------|
\ 2 / \ 2 /
$$x_{1} = - i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + 2$$
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/ 2 / / 2 \\ / 2 / / 2 \\
4 / / 2 \ 2 |atan2\(6 - re(y))*im(y) - im(y)*re(y), im (y) + (6 - re(y))*re(y)/| 4 / / 2 \ 2 |atan2\(6 - re(y))*im(y) - im(y)*re(y), im (y) + (6 - re(y))*re(y)/|
x2 = 2 + \/ \im (y) + (6 - re(y))*re(y)/ + ((6 - re(y))*im(y) - im(y)*re(y)) *cos|------------------------------------------------------------------| + I*\/ \im (y) + (6 - re(y))*re(y)/ + ((6 - re(y))*im(y) - im(y)*re(y)) *sin|------------------------------------------------------------------|
\ 2 / \ 2 /
$$x_{2} = i \sqrt[4]{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + 2$$
x2 = i*(((6 - re(y))*re(y) + im(y)^2)^2 + ((6 - re(y))*im(y) - re(y)*im(y))^2)^(1/4)*sin(atan2((6 - re(y))*im(y) - re(y)*im(y, (6 - re(y))*re(y) + im(y)^2)/2) + (((6 - re(y))*re(y) + im(y)^2)^2 + ((6 - re(y))*im(y) - re(y)*im(y))^2)^(1/4)*cos(atan2((6 - re(y))*im(y) - re(y)*im(y), (6 - re(y))*re(y) + im(y)^2)/2) + 2)
Suma y producto de raíces
[src]
suma
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/ 2 / / 2 \\ / 2 / / 2 \\ / 2 / / 2 \\ / 2 / / 2 \\
4 / / 2 \ 2 |atan2\-(-6 + re(y))*im(y) - im(y)*re(y), im (y) - (-6 + re(y))*re(y)/| 4 / / 2 \ 2 |atan2\-(-6 + re(y))*im(y) - im(y)*re(y), im (y) - (-6 + re(y))*re(y)/| 4 / / 2 \ 2 |atan2\(6 - re(y))*im(y) - im(y)*re(y), im (y) + (6 - re(y))*re(y)/| 4 / / 2 \ 2 |atan2\(6 - re(y))*im(y) - im(y)*re(y), im (y) + (6 - re(y))*re(y)/|
2 - \/ \im (y) - (-6 + re(y))*re(y)/ + (-(-6 + re(y))*im(y) - im(y)*re(y)) *cos|---------------------------------------------------------------------| - I*\/ \im (y) - (-6 + re(y))*re(y)/ + (-(-6 + re(y))*im(y) - im(y)*re(y)) *sin|---------------------------------------------------------------------| + 2 + \/ \im (y) + (6 - re(y))*re(y)/ + ((6 - re(y))*im(y) - im(y)*re(y)) *cos|------------------------------------------------------------------| + I*\/ \im (y) + (6 - re(y))*re(y)/ + ((6 - re(y))*im(y) - im(y)*re(y)) *sin|------------------------------------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(i \sqrt[4]{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + 2\right) + \left(- i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + 2\right)$$
=
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/ 2 / / 2 \\ / 2 / / 2 \\ / 2 / / 2 \\ / 2 / / 2 \\
4 / / 2 \ 2 |atan2\(6 - re(y))*im(y) - im(y)*re(y), im (y) + (6 - re(y))*re(y)/| 4 / / 2 \ 2 |atan2\-(-6 + re(y))*im(y) - im(y)*re(y), im (y) - (-6 + re(y))*re(y)/| 4 / / 2 \ 2 |atan2\(6 - re(y))*im(y) - im(y)*re(y), im (y) + (6 - re(y))*re(y)/| 4 / / 2 \ 2 |atan2\-(-6 + re(y))*im(y) - im(y)*re(y), im (y) - (-6 + re(y))*re(y)/|
4 + \/ \im (y) + (6 - re(y))*re(y)/ + ((6 - re(y))*im(y) - im(y)*re(y)) *cos|------------------------------------------------------------------| - \/ \im (y) - (-6 + re(y))*re(y)/ + (-(-6 + re(y))*im(y) - im(y)*re(y)) *cos|---------------------------------------------------------------------| + I*\/ \im (y) + (6 - re(y))*re(y)/ + ((6 - re(y))*im(y) - im(y)*re(y)) *sin|------------------------------------------------------------------| - I*\/ \im (y) - (-6 + re(y))*re(y)/ + (-(-6 + re(y))*im(y) - im(y)*re(y)) *sin|---------------------------------------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$i \sqrt[4]{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + 4$$
producto
/ _______________________________________________________________________ _______________________________________________________________________ \ / ____________________________________________________________________ ____________________________________________________________________ \ | / 2 / / 2 \\ / 2 / / 2 \\| | / 2 / / 2 \\ / 2 / / 2 \\| | 4 / / 2 \ 2 |atan2\-(-6 + re(y))*im(y) - im(y)*re(y), im (y) - (-6 + re(y))*re(y)/| 4 / / 2 \ 2 |atan2\-(-6 + re(y))*im(y) - im(y)*re(y), im (y) - (-6 + re(y))*re(y)/|| | 4 / / 2 \ 2 |atan2\(6 - re(y))*im(y) - im(y)*re(y), im (y) + (6 - re(y))*re(y)/| 4 / / 2 \ 2 |atan2\(6 - re(y))*im(y) - im(y)*re(y), im (y) + (6 - re(y))*re(y)/|| |2 - \/ \im (y) - (-6 + re(y))*re(y)/ + (-(-6 + re(y))*im(y) - im(y)*re(y)) *cos|---------------------------------------------------------------------| - I*\/ \im (y) - (-6 + re(y))*re(y)/ + (-(-6 + re(y))*im(y) - im(y)*re(y)) *sin|---------------------------------------------------------------------||*|2 + \/ \im (y) + (6 - re(y))*re(y)/ + ((6 - re(y))*im(y) - im(y)*re(y)) *cos|------------------------------------------------------------------| + I*\/ \im (y) + (6 - re(y))*re(y)/ + ((6 - re(y))*im(y) - im(y)*re(y)) *sin|------------------------------------------------------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(i \sqrt[4]{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + 2\right) \left(- i \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{im}{\left(y\right)} - \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)} - 6\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)} + 2\right)$$
=
2 2 4 + re (y) - im (y) - 6*re(y) - 6*I*im(y) + 2*I*im(y)*re(y)
$$\left(\operatorname{re}{\left(y\right)}\right)^{2} + 2 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 6 i \operatorname{im}{\left(y\right)} + 4$$
4 + re(y)^2 - im(y)^2 - 6*re(y) - 6*i*im(y) + 2*i*im(y)*re(y)