Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
-
Ecuación x^2-14*x+33=0
-
Ecuación x+18=8
- Expresar {x} en función de y en la ecuación:
- 12*x+1*y=15
- -17*x-12*y=-9
- 18*x+17*y=-14
- 16*x-17*y=-15
-
Expresiones idénticas
- -log(y)+log(y^ dos + uno)/ dos =Const-log(x^ dos + uno)/ dos
- menos logaritmo de (y) más logaritmo de (y al cuadrado más 1) dividir por 2 es igual a Const menos logaritmo de (x al cuadrado más 1) dividir por 2
- menos logaritmo de (y) más logaritmo de (y en el grado dos más uno) dividir por dos es igual a Const menos logaritmo de (x en el grado dos más uno) dividir por dos
- -log(y)+log(y2+1)/2=Const-log(x2+1)/2
- -logy+logy2+1/2=Const-logx2+1/2
- -log(y)+log(y²+1)/2=Const-log(x²+1)/2
- -log(y)+log(y en el grado 2+1)/2=Const-log(x en el grado 2+1)/2
- -logy+logy^2+1/2=Const-logx^2+1/2
- -log(y)+log(y^2+1) dividir por 2=Const-log(x^2+1) dividir por 2
-
Expresiones semejantes
- -log(y)+log(y^2-1)/2=Const-log(x^2+1)/2
- -log(y)+log(y^2+1)/2=Const+log(x^2+1)/2
- log(y)+log(y^2+1)/2=Const-log(x^2+1)/2
- -log(y)-log(y^2+1)/2=Const-log(x^2+1)/2
- -log(y)+log(y^2+1)/2=Const-log(x^2-1)/2
-
Expresiones con funciones
- Logaritmo log
- log^24x−log4x^3+2=0
- log(4^x-b,2)=0
- log(1/6)*(x-5)=x+1
- log_2(3)=log_x(x^(2)-1)
- log(sin(x))-3*cos(x)=0
- Logaritmo log
- log^24x−log4x^3+2=0
- log(4^x-b,2)=0
- log(1/6)*(x-5)=x+1
- log_2(3)=log_x(x^(2)-1)
- log(sin(x))-3*cos(x)=0
- Logaritmo log
- log^24x−log4x^3+2=0
- log(4^x-b,2)=0
- log(1/6)*(x-5)=x+1
- log_2(3)=log_x(x^(2)-1)
- log(sin(x))-3*cos(x)=0
-log(y)+log(y^2+1)/2=Const-log(x^2+1)/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 2 \ / 2 \
log\y + 1/ log\x + 1/
-log(y) + ----------- = c - -----------
2 2
$$- \log{\left(y \right)} + \frac{\log{\left(y^{2} + 1 \right)}}{2} = c - \frac{\log{\left(x^{2} + 1 \right)}}{2}$$
Gráfica
Respuesta rápida
[src]
/ // / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \\ / // / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \\
| |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)|| | |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)||
_____________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|---------------------------------------------------- - --------------------------------------------------, ---------------------------------------------------------- + --------------------------------------------|| _____________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|---------------------------------------------------- - --------------------------------------------------, ---------------------------------------------------------- + --------------------------------------------||
/ 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||
/ // / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ \ // 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ \ // 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||
/ |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y)| |\1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y)| |\1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /|
x1 = / |---------------------------------------------------- - --------------------------------------------------| + |---------------------------------------------------------- + --------------------------------------------| *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I* / |---------------------------------------------------- - --------------------------------------------------| + |---------------------------------------------------------- + --------------------------------------------| *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
/ | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 /
4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 |
\/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /
$$x_{1} = i \sqrt[4]{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)}$$
/ / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \\ / / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \\
| | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)|| | | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)||
_________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|- ----------------------------------------------------- + -------------------------------------------------, - --------------------------------------------------------- - ---------------------------------------------|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|- ----------------------------------------------------- + -------------------------------------------------, - --------------------------------------------------------- - ---------------------------------------------||
/ 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||
/ / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ \ / / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ \ / / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||
/ | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y)| | \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y)| | \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /|
x2 = - / |- ----------------------------------------------------- + -------------------------------------------------| + |- --------------------------------------------------------- - ---------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - I* / |- ----------------------------------------------------- + -------------------------------------------------| + |- --------------------------------------------------------- - ---------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
/ | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 /
4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 |
\/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /
$$x_{2} = - i \sqrt[4]{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)}$$
x2 = -i*((-(2*re(y)*im(y) - im(y^2*exp(2*c)))*(re(y)^2 - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) + 2*(re(y)^2 - re(y^2*exp(2*c)) - im(y)^2 + 1)*re(y)*im(y)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2))^2 + (-2*(2*re(y)*im(y) - im(y^2*exp(2*c)))*re(y)*im(y)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) - (re(y)^2 - im(y)^2 + 1)*(re(y)^2 - re(y^2*exp(2*c)) - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2))^2)^(1/4)*sin(atan2(-(2*re(y)*im(y) - im(y^2*exp(2*c)))*(re(y)^2 - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) + 2*(re(y)^2 - re(y^2*exp(2*c)) - im(y)^2 + 1)*re(y)*im(y)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2, -2*(2*re(y)*im(y) - im(y^2*exp(2*c)))*re(y)*im(y)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) - (re(y)^2 - im(y)^2 + 1)*(re(y)^2 - re(y^2*exp(2*c)) - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2))/2) - ((-(2*re(y)*im(y) - im(y^2*exp(2*c)))*(re(y)^2 - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) + 2*(re(y)^2 - re(y^2*exp(2*c)) - im(y)^2 + 1)*re(y)*im(y)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2))^2 + (-2*(2*re(y)*im(y) - im(y^2*exp(2*c)))*re(y)*im(y)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) - (re(y)^2 - im(y)^2 + 1)*(re(y)^2 - re(y^2*exp(2*c)) - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2))^2)^(1/4)*cos(atan2(-(2*re(y)*im(y) - im(y^2*exp(2*c)))*(re(y)^2 - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) + 2*(re(y)^2 - re(y^2*exp(2*c)) - im(y)^2 + 1)*re(y)*im(y)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2), -2*(2*re(y)*im(y) - im(y^2*exp(2*c)))*re(y)*im(y)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) - (re(y)^2 - im(y)^2 + 1)*(re(y)^2 - re(y^2*exp(2*c)) - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2))/2))
Suma y producto de raíces
[src]
suma
/ // / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \\ / // / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \\ / / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \\ / / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \\
| |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)|| | |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)|| | | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)|| | | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)||
_____________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|---------------------------------------------------- - --------------------------------------------------, ---------------------------------------------------------- + --------------------------------------------|| _____________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|---------------------------------------------------- - --------------------------------------------------, ---------------------------------------------------------- + --------------------------------------------|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|- ----------------------------------------------------- + -------------------------------------------------, - --------------------------------------------------------- - ---------------------------------------------|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|- ----------------------------------------------------- + -------------------------------------------------, - --------------------------------------------------------- - ---------------------------------------------||
/ 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*c\\ / 2 2 \ / 2 2 / 2 2*c\\ \ // 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ \ // 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ \ / / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ \ / / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||
/ |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y)| |\1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y)| |\1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y)| | \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y)| | \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /|
/ |---------------------------------------------------- - --------------------------------------------------| + |---------------------------------------------------------- + --------------------------------------------| *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I* / |---------------------------------------------------- - --------------------------------------------------| + |---------------------------------------------------------- + --------------------------------------------| *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + - / |- ----------------------------------------------------- + -------------------------------------------------| + |- --------------------------------------------------------- - ---------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - I* / |- ----------------------------------------------------- + -------------------------------------------------| + |- --------------------------------------------------------- - ---------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
/ | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 /
4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 |
\/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /
$$\left(i \sqrt[4]{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)}\right) + \left(- i \sqrt[4]{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)}\right)$$
=
/ // / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \\ / / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \\ / // / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \\ / / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \\
| |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)|| | | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)|| | |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)|| | | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)||
_____________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|---------------------------------------------------- - --------------------------------------------------, ---------------------------------------------------------- + --------------------------------------------|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|- ----------------------------------------------------- + -------------------------------------------------, - --------------------------------------------------------- - ---------------------------------------------|| _____________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|---------------------------------------------------- - --------------------------------------------------, ---------------------------------------------------------- + --------------------------------------------|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|- ----------------------------------------------------- + -------------------------------------------------, - --------------------------------------------------------- - ---------------------------------------------||
/ 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*c\\ / 2 2 \ / 2 2 / 2 2*c\\ \ // 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ \ / / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ \ // 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ \ / / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||
/ |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y)| |\1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y)| | \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y)| |\1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y)| | \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /|
/ |---------------------------------------------------- - --------------------------------------------------| + |---------------------------------------------------------- + --------------------------------------------| *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - / |- ----------------------------------------------------- + -------------------------------------------------| + |- --------------------------------------------------------- - ---------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I* / |---------------------------------------------------- - --------------------------------------------------| + |---------------------------------------------------------- + --------------------------------------------| *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - I* / |- ----------------------------------------------------- + -------------------------------------------------| + |- --------------------------------------------------------- - ---------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
/ | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 /
4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 |
\/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /
$$i \sqrt[4]{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} - i \sqrt[4]{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)}$$
producto
/ / // / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \\ / // / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \\\ / / / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \\ / / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \\\ | | |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)|| | |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)||| | | | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)|| | | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)||| | _____________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|---------------------------------------------------- - --------------------------------------------------, ---------------------------------------------------------- + --------------------------------------------|| _____________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|---------------------------------------------------- - --------------------------------------------------, ---------------------------------------------------------- + --------------------------------------------||| | _________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|- ----------------------------------------------------- + -------------------------------------------------, - --------------------------------------------------------- - ---------------------------------------------|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|- ----------------------------------------------------- + -------------------------------------------------, - --------------------------------------------------------- - ---------------------------------------------||| | / 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*c\\ / 2 2 \ / 2 2 / 2 2*c\\ \ // 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // / 2 2*c\\ / 2 2 \ / 2 2 / 2 2*c\\ \ // 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\\ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||| | / / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ \ / / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / / / / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ \ / / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||| | / |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y)| |\1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / |\-2*im(y)*re(y) + im\y *e //*\1 + re (y) - im (y)/ 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y)| |\1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // 2*\-2*im(y)*re(y) + im\y *e //*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /|| | / | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y)| | \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / | \- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y)| | \1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)| | \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /|| | / |---------------------------------------------------- - --------------------------------------------------| + |---------------------------------------------------------- + --------------------------------------------| *cos|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I* / |---------------------------------------------------- - --------------------------------------------------| + |---------------------------------------------------------- + --------------------------------------------| *sin|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||*|- / |- ----------------------------------------------------- + -------------------------------------------------| + |- --------------------------------------------------------- - ---------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - I* / |- ----------------------------------------------------- + -------------------------------------------------| + |- --------------------------------------------------------- - ---------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| | / | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 /| | / | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 /| |4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | | | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | | \\/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / / \ \/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / /
$$\left(i \sqrt[4]{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{2 \left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)}\right) \left(- i \sqrt[4]{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)}\right)$$
=
/ // / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ \ / / 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \ \
|-\\- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ + 2*\-1 + im (y) - re (y) + re\y *e //*im(y)*re(y)/ -\- \1 + re (y) - im (y)/*\-1 + im (y) - re (y) + re\y *e // + 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)/ |
I*atan2|--------------------------------------------------------------------------------------------------------------, ----------------------------------------------------------------------------------------------------------------|
_____________________________________________________________________________________________________________________________________________________________________________________________________________________________ | 2 2 |
/ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2 |
/ // / 2 2*c\ \ / 2 2 \ / 2 2 / 2 2*c\\ \ // 2 2 \ / 2 2 / 2 2*c\\ / / 2 2*c\ \ \ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /
-\/ \\- im\y *e / + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ - 2*\1 + re (y) - im (y) - re\y *e //*im(y)*re(y)/ + \\1 + re (y) - im (y)/*\1 + re (y) - im (y) - re\y *e // + 2*\- im\y *e / + 2*im(y)*re(y)/*im(y)*re(y)/ *e
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2 2 \ 2 2
\1 + re (y) - im (y)/ + 4*im (y)*re (y)
$$- \frac{\sqrt{\left(\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) - 2 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \operatorname{re}{\left(y^{2} e^{2 c}\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)\right)^{2}} e^{i \operatorname{atan_{2}}{\left(- \frac{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) + 2 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},- \frac{2 \left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(y^{2} e^{2 c}\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(y^{2} e^{2 c}\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}$$
-sqrt(((-im(y^2*exp(2*c)) + 2*im(y)*re(y))*(1 + re(y)^2 - im(y)^2) - 2*(1 + re(y)^2 - im(y)^2 - re(y^2*exp(2*c)))*im(y)*re(y))^2 + ((1 + re(y)^2 - im(y)^2)*(1 + re(y)^2 - im(y)^2 - re(y^2*exp(2*c))) + 2*(-im(y^2*exp(2*c)) + 2*im(y)*re(y))*im(y)*re(y))^2)*exp(i*atan2(-((-im(y^2*exp(2*c)) + 2*im(y)*re(y))*(1 + re(y)^2 - im(y)^2) + 2*(-1 + im(y)^2 - re(y)^2 + re(y^2*exp(2*c)))*im(y)*re(y))/((1 + re(y)^2 - im(y)^2)^2 + 4*im(y)^2*re(y)^2), -(-(1 + re(y)^2 - im(y)^2)*(-1 + im(y)^2 - re(y)^2 + re(y^2*exp(2*c))) + 2*(-im(y^2*exp(2*c)) + 2*im(y)*re(y))*im(y)*re(y))/((1 + re(y)^2 - im(y)^2)^2 + 4*im(y)^2*re(y)^2)))/((1 + re(y)^2 - im(y)^2)^2 + 4*im(y)^2*re(y)^2)