Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación (x+9)^2=36*x
-
Ecuación a+120=2000/5
-
Ecuación (|x|)=6
-
Ecuación 6*x=12
- Expresar {x} en función de y en la ecuación:
- -6*x-12*y=9
- 9*x-1*y=17
- 10*x-2*y=11
- 12*x-3*y=-2
-
Expresiones idénticas
- log(y^ dos + tres)/ dos =log(x^ dos + dos)/ tres
- logaritmo de (y al cuadrado más 3) dividir por 2 es igual a logaritmo de (x al cuadrado más 2) dividir por 3
- logaritmo de (y en el grado dos más tres) dividir por dos es igual a logaritmo de (x en el grado dos más dos) dividir por tres
- log(y2+3)/2=log(x2+2)/3
- logy2+3/2=logx2+2/3
- log(y²+3)/2=log(x²+2)/3
- log(y en el grado 2+3)/2=log(x en el grado 2+2)/3
- logy^2+3/2=logx^2+2/3
- log(y^2+3) dividir por 2=log(x^2+2) dividir por 3
-
Expresiones semejantes
- log(y^2-3)/2=log(x^2+2)/3
- log(y^2+3)/2=log(x^2-2)/3
-
Expresiones con funciones
- Logaritmo log
- log_8(4^(x^2-1)-1)+2/3=log_8(2^(x^2+2)-7)
- log(cos4pi)=|9+a-x|
- log(x-3)/log(2)=4
- log2(x^2-2x+5)=2sin(pix/2)
- logsqrt(x)(4x^2+3x)=0
- Logaritmo log
- log_8(4^(x^2-1)-1)+2/3=log_8(2^(x^2+2)-7)
- log(cos4pi)=|9+a-x|
- log(x-3)/log(2)=4
- log2(x^2-2x+5)=2sin(pix/2)
- logsqrt(x)(4x^2+3x)=0
log(y^2+3)/2=log(x^2+2)/3 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 2 \ / 2 \
log\y + 3/ log\x + 2/
----------- = -----------
2 3
$$\frac{\log{\left(y^{2} + 3 \right)}}{2} = \frac{\log{\left(x^{2} + 2 \right)}}{3}$$
Gráfica
Respuesta rápida
[src]
__________________________________________________________________________________________________________________________________________________________________________________________________________ / / 3/4 3/4 \\ __________________________________________________________________________________________________________________________________________________________________________________________________________ / / 3/4 3/4 \\
/ 2 | |/ 2 \ / / 2 2 \\ / 2 \ / / 2 2 \\|| / 2 | |/ 2 \ / / 2 2 \\ / 2 \ / / 2 2 \\||
/ / 3/4 \ 3/2 | ||/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/||| / / 3/4 \ 3/2 | ||/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|||
/ | / 2 \ / / 2 2 \\| / 2 \ / / 2 2 \\ |atan2|\\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin|-------------------------------------------|, -2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------||| / | / 2 \ / / 2 2 \\| / 2 \ / / 2 2 \\ |atan2|\\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin|-------------------------------------------|, -2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|||
/ | |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|| |/ 2 2 \ 2 2 | 2|3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| | \ \ 2 / \ 2 //| / | |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|| |/ 2 2 \ 2 2 | 2|3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| | \ \ 2 / \ 2 //|
x1 = - 4 / |-2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|| + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin |-------------------------------------------| *cos|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - I*4 / |-2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|| + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin |-------------------------------------------| *sin|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\/ \ \ 2 // \ 2 / \ 2 / \/ \ \ 2 // \ 2 / \ 2 /
$$x_{1} = - i \sqrt[4]{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2\right)^{2} + \left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{2}} \sin^{2}{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)},\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2 \right)}}{2} \right)} - \sqrt[4]{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2\right)^{2} + \left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{2}} \sin^{2}{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)},\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2 \right)}}{2} \right)}$$
__________________________________________________________________________________________________________________________________________________________________________________________________________ / / 3/4 3/4 \\ __________________________________________________________________________________________________________________________________________________________________________________________________________ / / 3/4 3/4 \\
/ 2 | |/ 2 \ / / 2 2 \\ / 2 \ / / 2 2 \\|| / 2 | |/ 2 \ / / 2 2 \\ / 2 \ / / 2 2 \\||
/ / 3/4 \ 3/2 | ||/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/||| / / 3/4 \ 3/2 | ||/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|||
/ | / 2 \ / / 2 2 \\| / 2 \ / / 2 2 \\ |atan2|\\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin|-------------------------------------------|, -2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------||| / | / 2 \ / / 2 2 \\| / 2 \ / / 2 2 \\ |atan2|\\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin|-------------------------------------------|, -2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|||
/ | |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|| |/ 2 2 \ 2 2 | 2|3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| | \ \ 2 / \ 2 //| / | |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|| |/ 2 2 \ 2 2 | 2|3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| | \ \ 2 / \ 2 //|
x2 = 4 / |-2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|| + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin |-------------------------------------------| *cos|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*4 / |-2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|| + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin |-------------------------------------------| *sin|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\/ \ \ 2 // \ 2 / \ 2 / \/ \ \ 2 // \ 2 / \ 2 /
$$x_{2} = i \sqrt[4]{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2\right)^{2} + \left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{2}} \sin^{2}{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)},\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2\right)^{2} + \left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{2}} \sin^{2}{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)},\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2 \right)}}{2} \right)}$$
x2 = i*((((re(y)^2 - im(y)^2 + 3)^2 + 4*re(y)^2*im(y)^2)^(3/4)*cos(3*atan2(2*re(y)*im(y, re(y)^2 - im(y)^2 + 3)/2) - 2)^2 + ((re(y)^2 - im(y)^2 + 3)^2 + 4*re(y)^2*im(y)^2)^(3/2)*sin(3*atan2(2*re(y)*im(y), re(y)^2 - im(y)^2 + 3)/2)^2)^(1/4)*sin(atan2(((re(y)^2 - im(y)^2 + 3)^2 + 4*re(y)^2*im(y)^2)^(3/4)*sin(3*atan2(2*re(y)*im(y), re(y)^2 - im(y)^2 + 3)/2), ((re(y)^2 - im(y)^2 + 3)^2 + 4*re(y)^2*im(y)^2)^(3/4)*cos(3*atan2(2*re(y)*im(y), re(y)^2 - im(y)^2 + 3)/2) - 2)/2) + ((((re(y)^2 - im(y)^2 + 3)^2 + 4*re(y)^2*im(y)^2)^(3/4)*cos(3*atan2(2*re(y)*im(y), re(y)^2 - im(y)^2 + 3)/2) - 2)^2 + ((re(y)^2 - im(y)^2 + 3)^2 + 4*re(y)^2*im(y)^2)^(3/2)*sin(3*atan2(2*re(y)*im(y), re(y)^2 - im(y)^2 + 3)/2)^2)^(1/4)*cos(atan2(((re(y)^2 - im(y)^2 + 3)^2 + 4*re(y)^2*im(y)^2)^(3/4)*sin(3*atan2(2*re(y)*im(y), re(y)^2 - im(y)^2 + 3)/2), ((re(y)^2 - im(y)^2 + 3)^2 + 4*re(y)^2*im(y)^2)^(3/4)*cos(3*atan2(2*re(y)*im(y), re(y)^2 - im(y)^2 + 3)/2) - 2)/2))
Suma y producto de raíces
[src]
suma
__________________________________________________________________________________________________________________________________________________________________________________________________________ / / 3/4 3/4 \\ __________________________________________________________________________________________________________________________________________________________________________________________________________ / / 3/4 3/4 \\ __________________________________________________________________________________________________________________________________________________________________________________________________________ / / 3/4 3/4 \\ __________________________________________________________________________________________________________________________________________________________________________________________________________ / / 3/4 3/4 \\
/ 2 | |/ 2 \ / / 2 2 \\ / 2 \ / / 2 2 \\|| / 2 | |/ 2 \ / / 2 2 \\ / 2 \ / / 2 2 \\|| / 2 | |/ 2 \ / / 2 2 \\ / 2 \ / / 2 2 \\|| / 2 | |/ 2 \ / / 2 2 \\ / 2 \ / / 2 2 \\||
/ / 3/4 \ 3/2 | ||/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/||| / / 3/4 \ 3/2 | ||/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/||| / / 3/4 \ 3/2 | ||/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/||| / / 3/4 \ 3/2 | ||/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|||
/ | / 2 \ / / 2 2 \\| / 2 \ / / 2 2 \\ |atan2|\\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin|-------------------------------------------|, -2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------||| / | / 2 \ / / 2 2 \\| / 2 \ / / 2 2 \\ |atan2|\\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin|-------------------------------------------|, -2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------||| / | / 2 \ / / 2 2 \\| / 2 \ / / 2 2 \\ |atan2|\\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin|-------------------------------------------|, -2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------||| / | / 2 \ / / 2 2 \\| / 2 \ / / 2 2 \\ |atan2|\\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin|-------------------------------------------|, -2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|||
/ | |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|| |/ 2 2 \ 2 2 | 2|3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| | \ \ 2 / \ 2 //| / | |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|| |/ 2 2 \ 2 2 | 2|3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| | \ \ 2 / \ 2 //| / | |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|| |/ 2 2 \ 2 2 | 2|3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| | \ \ 2 / \ 2 //| / | |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|| |/ 2 2 \ 2 2 | 2|3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| | \ \ 2 / \ 2 //|
- 4 / |-2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|| + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin |-------------------------------------------| *cos|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - I*4 / |-2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|| + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin |-------------------------------------------| *sin|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + 4 / |-2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|| + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin |-------------------------------------------| *cos|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*4 / |-2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|| + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin |-------------------------------------------| *sin|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\/ \ \ 2 // \ 2 / \ 2 / \/ \ \ 2 // \ 2 / \ 2 / \/ \ \ 2 // \ 2 / \ 2 / \/ \ \ 2 // \ 2 / \ 2 /
$$\left(- i \sqrt[4]{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2\right)^{2} + \left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{2}} \sin^{2}{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)},\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2 \right)}}{2} \right)} - \sqrt[4]{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2\right)^{2} + \left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{2}} \sin^{2}{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)},\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2 \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2\right)^{2} + \left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{2}} \sin^{2}{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)},\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2\right)^{2} + \left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{2}} \sin^{2}{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)},\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2 \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ __________________________________________________________________________________________________________________________________________________________________________________________________________ / / 3/4 3/4 \\ __________________________________________________________________________________________________________________________________________________________________________________________________________ / / 3/4 3/4 \\\ / __________________________________________________________________________________________________________________________________________________________________________________________________________ / / 3/4 3/4 \\ __________________________________________________________________________________________________________________________________________________________________________________________________________ / / 3/4 3/4 \\\ | / 2 | |/ 2 \ / / 2 2 \\ / 2 \ / / 2 2 \\|| / 2 | |/ 2 \ / / 2 2 \\ / 2 \ / / 2 2 \\||| | / 2 | |/ 2 \ / / 2 2 \\ / 2 \ / / 2 2 \\|| / 2 | |/ 2 \ / / 2 2 \\ / 2 \ / / 2 2 \\||| | / / 3/4 \ 3/2 | ||/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/||| / / 3/4 \ 3/2 | ||/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|||| | / / 3/4 \ 3/2 | ||/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/||| / / 3/4 \ 3/2 | ||/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|||| | / | / 2 \ / / 2 2 \\| / 2 \ / / 2 2 \\ |atan2|\\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin|-------------------------------------------|, -2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------||| / | / 2 \ / / 2 2 \\| / 2 \ / / 2 2 \\ |atan2|\\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin|-------------------------------------------|, -2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|||| | / | / 2 \ / / 2 2 \\| / 2 \ / / 2 2 \\ |atan2|\\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin|-------------------------------------------|, -2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------||| / | / 2 \ / / 2 2 \\| / 2 \ / / 2 2 \\ |atan2|\\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin|-------------------------------------------|, -2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|||| | / | |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|| |/ 2 2 \ 2 2 | 2|3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| | \ \ 2 / \ 2 //| / | |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|| |/ 2 2 \ 2 2 | 2|3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| | \ \ 2 / \ 2 //|| | / | |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|| |/ 2 2 \ 2 2 | 2|3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| | \ \ 2 / \ 2 //| / | |/ 2 2 \ 2 2 | |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|| |/ 2 2 \ 2 2 | 2|3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| | \ \ 2 / \ 2 //|| |- 4 / |-2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|| + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin |-------------------------------------------| *cos|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - I*4 / |-2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|| + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin |-------------------------------------------| *sin|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||*|4 / |-2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|| + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin |-------------------------------------------| *cos|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*4 / |-2 + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *cos|-------------------------------------------|| + \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *sin |-------------------------------------------| *sin|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| \ \/ \ \ 2 // \ 2 / \ 2 / \/ \ \ 2 // \ 2 / \ 2 // \\/ \ \ 2 // \ 2 / \ 2 / \/ \ \ 2 // \ 2 / \ 2 //
$$\left(- i \sqrt[4]{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2\right)^{2} + \left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{2}} \sin^{2}{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)},\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2 \right)}}{2} \right)} - \sqrt[4]{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2\right)^{2} + \left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{2}} \sin^{2}{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)},\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2 \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2\right)^{2} + \left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{2}} \sin^{2}{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)},\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2 \right)}}{2} \right)} + \sqrt[4]{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2\right)^{2} + \left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{2}} \sin^{2}{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)},\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} - 2 \right)}}{2} \right)}\right)$$
=
/ / 2 2 \ / 2 2 \\
| 3/4 -3*I*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/ 3/4 -3*I*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/|
| / 2 \ / / 2 2 \\ ---------------------------------------------- / 2 \ / / 2 2 \\ ----------------------------------------------|
| |/ 2 2 \ 2 2 | | 3*I*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| 2 |/ 2 2 \ 2 2 | | 3*I*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| 2 |
_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |-I*\\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *\-1 + e /*e \\3 + re (y) - im (y)/ + 4*im (y)*re (y)/ *\1 + e /*e |
/ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ 3/4 / / 2 2 \\ _____________________________________________________________ _____________________________________________________________ I*atan2|-------------------------------------------------------------------------------------------------------------------------------------------------------, -2 + --------------------------------------------------------------------------------------------------------------------------------------------------|
/ / 4 4 2 2 2 2 / 4 4 2 2 2 2 4 / 4 4 2 2 2 2 4 / 4 4 2 2 2 2 2 / 4 4 2 2 2 2 \ |3*atan2\2*im(y)*re(y), 3 + re (y) - im (y)/| / 4 4 2 2 2 2 2 / 4 4 2 2 2 2 2 2 \ 2 2 /
- / 4 + 9*\/ 9 + im (y) + re (y) - 6*im (y) + 6*re (y) + 2*im (y)*re (y) + \/ 9 + im (y) + re (y) - 6*im (y) + 6*re (y) + 2*im (y)*re (y) *im (y) + \/ 9 + im (y) + re (y) - 6*im (y) + 6*re (y) + 2*im (y)*re (y) *re (y) - 6*\/ 9 + im (y) + re (y) - 6*im (y) + 6*re (y) + 2*im (y)*re (y) *im (y) - 4*\9 + im (y) + re (y) - 6*im (y) + 6*re (y) + 2*im (y)*re (y)/ *cos|-------------------------------------------| + 6*\/ 9 + im (y) + re (y) - 6*im (y) + 6*re (y) + 2*im (y)*re (y) *re (y) + 2*\/ 9 + im (y) + re (y) - 6*im (y) + 6*re (y) + 2*im (y)*re (y) *im (y)*re (y) *e
\/ \ 2 /
$$- \sqrt{- 4 \left(\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 6 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4} - 6 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 9\right)^{\frac{3}{4}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2} \right)} + \sqrt{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 6 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4} - 6 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 9} \left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \sqrt{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 6 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4} - 6 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 9} \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 6 \sqrt{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 6 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4} - 6 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 9} \left(\operatorname{re}{\left(y\right)}\right)^{2} + \sqrt{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 6 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4} - 6 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 9} \left(\operatorname{im}{\left(y\right)}\right)^{4} - 6 \sqrt{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 6 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4} - 6 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 9} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 9 \sqrt{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 6 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4} - 6 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 9} + 4} e^{i \operatorname{atan_{2}}{\left(- \frac{i \left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \left(e^{3 i \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}} - 1\right) e^{- \frac{3 i \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2}}}{2},\frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{4}} \left(e^{3 i \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}} + 1\right) e^{- \frac{3 i \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 3 \right)}}{2}}}{2} - 2 \right)}}$$
-sqrt(4 + 9*sqrt(9 + im(y)^4 + re(y)^4 - 6*im(y)^2 + 6*re(y)^2 + 2*im(y)^2*re(y)^2) + sqrt(9 + im(y)^4 + re(y)^4 - 6*im(y)^2 + 6*re(y)^2 + 2*im(y)^2*re(y)^2)*im(y)^4 + sqrt(9 + im(y)^4 + re(y)^4 - 6*im(y)^2 + 6*re(y)^2 + 2*im(y)^2*re(y)^2)*re(y)^4 - 6*sqrt(9 + im(y)^4 + re(y)^4 - 6*im(y)^2 + 6*re(y)^2 + 2*im(y)^2*re(y)^2)*im(y)^2 - 4*(9 + im(y)^4 + re(y)^4 - 6*im(y)^2 + 6*re(y)^2 + 2*im(y)^2*re(y)^2)^(3/4)*cos(3*atan2(2*im(y)*re(y), 3 + re(y)^2 - im(y)^2)/2) + 6*sqrt(9 + im(y)^4 + re(y)^4 - 6*im(y)^2 + 6*re(y)^2 + 2*im(y)^2*re(y)^2)*re(y)^2 + 2*sqrt(9 + im(y)^4 + re(y)^4 - 6*im(y)^2 + 6*re(y)^2 + 2*im(y)^2*re(y)^2)*im(y)^2*re(y)^2)*exp(i*atan2(-i*((3 + re(y)^2 - im(y)^2)^2 + 4*im(y)^2*re(y)^2)^(3/4)*(-1 + exp(3*i*atan2(2*im(y)*re(y), 3 + re(y)^2 - im(y)^2)))*exp(-3*i*atan2(2*im(y)*re(y), 3 + re(y)^2 - im(y)^2)/2)/2, -2 + ((3 + re(y)^2 - im(y)^2)^2 + 4*im(y)^2*re(y)^2)^(3/4)*(1 + exp(3*i*atan2(2*im(y)*re(y), 3 + re(y)^2 - im(y)^2)))*exp(-3*i*atan2(2*im(y)*re(y), 3 + re(y)^2 - im(y)^2)/2)/2))