Sr Examen
Otras calculadoras
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¿Cómo usar?
- 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 -2*(-2-y)-y-2=0
- 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
- Factorizar el polinomio:
- y^2-x^2
-
Expresiones idénticas
- sqrt(4x-4x^ dos - uno)=y^ dos -x^ dos
- raíz cuadrada de (4x menos 4x al cuadrado menos 1) es igual a y al cuadrado menos x al cuadrado
- raíz cuadrada de (4x menos 4x en el grado dos menos uno) es igual a y en el grado dos menos x en el grado dos
- √(4x-4x^2-1)=y^2-x^2
- sqrt(4x-4x2-1)=y2-x2
- sqrt4x-4x2-1=y2-x2
- sqrt(4x-4x²-1)=y²-x²
- sqrt(4x-4x en el grado 2-1)=y en el grado 2-x en el grado 2
- sqrt4x-4x^2-1=y^2-x^2
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Expresiones semejantes
- sqrt(4x+4x^2-1)=y^2-x^2
- sqrt(4x-4x^2-1)=y^2+x^2
- sqrt(4x-4x^2+1)=y^2-x^2
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(14+5*x)=-x
- sqrt99×sinx-49cosx=51
- sqrt(x^2)=sqrt(-2x)
- sqrt(((0,9-0,3)*(0,9-0,3))+((2,5-0,9)*(2,5-0,9)))=x
- sqrt(x)=x^9
sqrt(4x-4x^2-1)=y^2-x^2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
________________ / 2 2 2 \/ 4*x - 4*x - 1 = y - x
$$\sqrt{\left(- 4 x^{2} + 4 x\right) - 1} = - x^{2} + y^{2}$$
Gráfica
Respuesta rápida
[src]
/ _________________________________________________ \ _________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| 4 / 2 / 2 2 \ |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|
x1 = I*|1 - \/ (-1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|-----------------------------------------------|| - \/ (-1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *cos|-----------------------------------------------|
\ \ 2 // \ 2 /
$$x_{1} = i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}$$
/ _________________________________________________ \ _________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| 4 / 2 / 2 2 \ |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|
x2 = I*|1 + \/ (-1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|-----------------------------------------------|| + \/ (-1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *cos|-----------------------------------------------|
\ \ 2 // \ 2 /
$$x_{2} = i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}$$
/ ________________________________________________ \ ________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| 4 / 2 / 2 2 \ |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|
x3 = I*|-1 - \/ (1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|----------------------------------------------|| - \/ (1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *cos|----------------------------------------------|
\ \ 2 // \ 2 /
$$x_{3} = i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}$$
/ ________________________________________________ \ ________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| 4 / 2 / 2 2 \ |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|
x4 = I*|-1 + \/ (1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|----------------------------------------------|| + \/ (1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *cos|----------------------------------------------|
\ \ 2 // \ 2 /
$$x_{4} = i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}$$
x4 = i*(((2*re(y)*im(y) + 1)^2 + (re(y)^2 - im(y)^2 - 1)^2)^(1/4)*sin(atan2(2*re(y)*im(y + 1, re(y)^2 - im(y)^2 - 1)/2) - 1) + ((2*re(y)*im(y) + 1)^2 + (re(y)^2 - im(y)^2 - 1)^2)^(1/4)*cos(atan2(2*re(y)*im(y) + 1, re(y)^2 - im(y)^2 - 1)/2))
Suma y producto de raíces
[src]
suma
/ _________________________________________________ \ _________________________________________________ / _________________________________________________ \ _________________________________________________ / ________________________________________________ \ ________________________________________________ / ________________________________________________ \ ________________________________________________ | / 2 / / 2 2 \\| / 2 / / 2 2 \\ | / 2 / / 2 2 \\| / 2 / / 2 2 \\ | / 2 / / 2 2 \\| / 2 / / 2 2 \\ | / 2 / / 2 2 \\| / 2 / / 2 2 \\ | 4 / 2 / 2 2 \ |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| 4 / 2 / 2 2 \ |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/| | 4 / 2 / 2 2 \ |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| 4 / 2 / 2 2 \ |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/| | 4 / 2 / 2 2 \ |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| 4 / 2 / 2 2 \ |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/| | 4 / 2 / 2 2 \ |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| 4 / 2 / 2 2 \ |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/| I*|1 - \/ (-1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|-----------------------------------------------|| - \/ (-1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *cos|-----------------------------------------------| + I*|1 + \/ (-1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|-----------------------------------------------|| + \/ (-1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *cos|-----------------------------------------------| + I*|-1 - \/ (1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|----------------------------------------------|| - \/ (1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *cos|----------------------------------------------| + I*|-1 + \/ (1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|----------------------------------------------|| + \/ (1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *cos|----------------------------------------------| \ \ 2 // \ 2 / \ \ 2 // \ 2 / \ \ 2 // \ 2 / \ \ 2 // \ 2 /
$$\left(i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) + \left(\left(i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) + \left(\left(i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) + \left(i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right)\right)\right)$$
=
/ _________________________________________________ \ / _________________________________________________ \ / ________________________________________________ \ / ________________________________________________ \ | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | 4 / 2 / 2 2 \ |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| | 4 / 2 / 2 2 \ |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| | 4 / 2 / 2 2 \ |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| | 4 / 2 / 2 2 \ |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| I*|1 + \/ (-1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|-----------------------------------------------|| + I*|1 - \/ (-1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|-----------------------------------------------|| + I*|-1 + \/ (1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|----------------------------------------------|| + I*|-1 - \/ (1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|----------------------------------------------|| \ \ 2 // \ \ 2 // \ \ 2 // \ \ 2 //
$$i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) + i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) + i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) + i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right)$$
producto
/ / _________________________________________________ \ _________________________________________________ \ / / _________________________________________________ \ _________________________________________________ \ / / ________________________________________________ \ ________________________________________________ \ / / ________________________________________________ \ ________________________________________________ \ | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | 4 / 2 / 2 2 \ |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| 4 / 2 / 2 2 \ |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| | | 4 / 2 / 2 2 \ |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| 4 / 2 / 2 2 \ |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| | | 4 / 2 / 2 2 \ |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| 4 / 2 / 2 2 \ |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| | | 4 / 2 / 2 2 \ |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| 4 / 2 / 2 2 \ |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| |I*|1 - \/ (-1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|-----------------------------------------------|| - \/ (-1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *cos|-----------------------------------------------||*|I*|1 + \/ (-1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|-----------------------------------------------|| + \/ (-1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *cos|-----------------------------------------------||*|I*|-1 - \/ (1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|----------------------------------------------|| - \/ (1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *cos|----------------------------------------------||*|I*|-1 + \/ (1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *sin|----------------------------------------------|| + \/ (1 + 2*im(y)*re(y)) + \-1 + re (y) - im (y)/ *cos|----------------------------------------------|| \ \ \ 2 // \ 2 // \ \ \ 2 // \ 2 // \ \ \ 2 // \ 2 // \ \ \ 2 // \ 2 //
$$\left(i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) \left(i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) \left(i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) \left(i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right)$$
=
4 4 2 2 3 3 1 + im (y) + re (y) - 6*im (y)*re (y) - 4*I*im (y)*re(y) + 4*I*re (y)*im(y)
$$\left(\operatorname{re}{\left(y\right)}\right)^{4} + 4 i \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 6 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 4 i \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + \left(\operatorname{im}{\left(y\right)}\right)^{4} + 1$$
1 + im(y)^4 + re(y)^4 - 6*im(y)^2*re(y)^2 - 4*i*im(y)^3*re(y) + 4*i*re(y)^3*im(y)