Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
- Ecuación x^2-49=0
-
Ecuación 1-x/2=x/3
-
Ecuación 3*x^2-9=0
-
Ecuación -8x-17=3x-105
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- -19*x+14*y=20
- 5*x-14*y=-15
-
Expresiones idénticas
- log(y^ dos + uno)/ dos =c-log(x^ dos - uno)/ dos
- logaritmo de (y al cuadrado más 1) dividir por 2 es igual a c menos logaritmo de (x al cuadrado menos 1) dividir por 2
- logaritmo de (y en el grado dos más uno) dividir por dos es igual a c menos logaritmo de (x en el grado dos menos uno) dividir por dos
- log(y2+1)/2=c-log(x2-1)/2
- logy2+1/2=c-logx2-1/2
- log(y²+1)/2=c-log(x²-1)/2
- log(y en el grado 2+1)/2=c-log(x en el grado 2-1)/2
- logy^2+1/2=c-logx^2-1/2
- log(y^2+1) dividir por 2=c-log(x^2-1) dividir por 2
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Expresiones semejantes
- log(y^2+1)/2=c+log(x^2-1)/2
- log(y^2-1)/2=c-log(x^2-1)/2
- log(y^2+1)/2=c-log(x^2+1)/2
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Expresiones con funciones
- Logaritmo log
- log2x+2(25)=2
- log(1/2)*x=2*x+5
- log(2*y+1)/2=log(sin(x))
- log(1)/x*x^2=-1
- log(x+1)((x-1)(x^2+x-8))=log(x-1)((x+1)^3)
- Logaritmo log
- log2x+2(25)=2
- log(1/2)*x=2*x+5
- log(2*y+1)/2=log(sin(x))
- log(1)/x*x^2=-1
- log(x+1)((x-1)(x^2+x-8))=log(x-1)((x+1)^3)
log(y^2+1)/2=c-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/
----------- = c - -----------
2 2
$$\frac{\log{\left(y^{2} + 1 \right)}}{2} = c - \frac{\log{\left(x^{2} - 1 \right)}}{2}$$
Gráfica
Respuesta rápida
[src]
/ // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ / 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \\ / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ / 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \\
| |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 2*im(y)*re(y)/*im(y)*re(y)|| | |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 2*im(y)*re(y)/*im(y)*re(y)||
_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------- - -----------------------------------------------------------, ------------------------------------------------------------------- + -----------------------------------------------------|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------- - -----------------------------------------------------------, ------------------------------------------------------------------- + -----------------------------------------------------||
/ 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||
/ // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ \ // 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ \ // 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||
/ |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y)| |\1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 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) /| / |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y)| |\1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 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) /|
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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}} \right)}}{2} \right)} - \sqrt[4]{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}} \right)}}{2} \right)}$$
/ // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ / 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \\ / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ / 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \\
| |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 2*im(y)*re(y)/*im(y)*re(y)|| | |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 2*im(y)*re(y)/*im(y)*re(y)||
_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------- - -----------------------------------------------------------, ------------------------------------------------------------------- + -----------------------------------------------------|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------- - -----------------------------------------------------------, ------------------------------------------------------------------- + -----------------------------------------------------||
/ 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||
/ // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ \ // 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ \ // 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||
/ |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y)| |\1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 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) /| / |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y)| |\1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}} \right)}}{2} \right)} + \sqrt[4]{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}} \right)}}{2} \right)}$$
x2 = i*(((exp(2*re(c))*sin(2*im(c)) + 2*re(y)*im(y))*(re(y)^2 - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) - 2*(exp(2*re(c))*cos(2*im(c)) + re(y)^2 - 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*(exp(2*re(c))*sin(2*im(c)) + 2*re(y)*im(y))*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)*(exp(2*re(c))*cos(2*im(c)) + re(y)^2 - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2))^2)^(1/4)*sin(atan2((exp(2*re(c))*sin(2*im(c)) + 2*re(y)*im(y))*(re(y)^2 - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) - 2*(exp(2*re(c))*cos(2*im(c)) + re(y)^2 - im(y)^2 + 1)*re(y)*im(y)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2, 2*(exp(2*re(c))*sin(2*im(c)) + 2*re(y)*im(y))*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)*(exp(2*re(c))*cos(2*im(c)) + re(y)^2 - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2))/2) + (((exp(2*re(c))*sin(2*im(c)) + 2*re(y)*im(y))*(re(y)^2 - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) - 2*(exp(2*re(c))*cos(2*im(c)) + re(y)^2 - 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*(exp(2*re(c))*sin(2*im(c)) + 2*re(y)*im(y))*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)*(exp(2*re(c))*cos(2*im(c)) + re(y)^2 - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2))^2)^(1/4)*cos(atan2((exp(2*re(c))*sin(2*im(c)) + 2*re(y)*im(y))*(re(y)^2 - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) - 2*(exp(2*re(c))*cos(2*im(c)) + re(y)^2 - im(y)^2 + 1)*re(y)*im(y)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2), 2*(exp(2*re(c))*sin(2*im(c)) + 2*re(y)*im(y))*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)*(exp(2*re(c))*cos(2*im(c)) + re(y)^2 - 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*re(c) \ / 2 2 \ / 2 2 2*re(c)\ / 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \\ / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ / 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \\ / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ / 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \\ / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ / 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \\
| |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 2*im(y)*re(y)/*im(y)*re(y)|| | |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 2*im(y)*re(y)/*im(y)*re(y)|| | |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 2*im(y)*re(y)/*im(y)*re(y)|| | |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 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*re(c) \ / 2 2 \ / 2 2 2*re(c)\ \ // 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ \ // 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ \ // 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ \ // 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||
/ |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y)| |\1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 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) /| / |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y)| |\1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 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) /| / |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y)| |\1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 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) /| / |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y)| |\1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}} \right)}}{2} \right)} - \sqrt[4]{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}} \right)}}{2} \right)} + \sqrt[4]{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}} \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ / 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \\ / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ / 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \\\ / / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ / 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \\ / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ / 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \\\ | | |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 2*im(y)*re(y)/*im(y)*re(y)|| | |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 2*im(y)*re(y)/*im(y)*re(y)||| | | |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 2*im(y)*re(y)/*im(y)*re(y)|| | |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y) \1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 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*re(c) \ / 2 2 \ / 2 2 2*re(c)\ \ // 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ \ // 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||| | / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ \ // 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ \ // 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||| | / |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y)| |\1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 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) /| / |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y)| |\1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 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) /|| | / |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y)| |\1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 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) /| / |\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y)| |\1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / 2*\e *sin(2*im(c)) + 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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}} \right)}}{2} \right)} - \sqrt[4]{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}} \right)}}{2} \right)} + \sqrt[4]{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \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}} \right)}}{2} \right)}\right)$$
=
/ / / 4*I*im(c)\ -2*I*im(c) 2 / 4*I*im(c)\ -2*I*im(c) 2 / 4*I*im(c)\ -2*I*im(c)\ / / 4*I*im(c)\ 2*re(c) -2*I*im(c)\ / / 4*I*im(c)\ 2*re(c) -2*I*im(c)\ \
| |I*\-1 + e /*e / 4*I*im(c)\ -2*I*im(c) I*re (y)*\-1 + e /*e I*im (y)*\-1 + e /*e | 2*re(c) / 2 2 \ | 2 2 \1 + e /*e *e | | I*\-1 + e /*e *e | |
|-|------------------------------- + \1 + e /*e *im(y)*re(y) + -------------------------------------- - --------------------------------------|*e \1 + re (y) - im (y)/*|1 + re (y) - im (y) + -------------------------------------| - 2*|-2*im(y)*re(y) + ----------------------------------------|*im(y)*re(y)|
| \ 2 2 2 / \ 2 / \ 2 / |
I*atan2|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------, ---------------------------------------------------------------------------------------------------------------------------------------------------------------|
_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | 4 4 2 2 2 2 2 |
/ 2 2 | 1 + im (y) + re (y) - 2*im (y) + 2*re (y) + 2*im (y)*re (y) / 2 2 \ 2 2 |
/ // 2*re(c) \ / 2 2 \ / 2 2 2*re(c)\ \ // 2 2 \ / 2 2 2*re(c)\ / 2*re(c) \ \ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) /
-\/ \\e *sin(2*im(c)) + 2*im(y)*re(y)/*\1 + re (y) - im (y)/ - 2*\1 + re (y) - im (y) + cos(2*im(c))*e /*im(y)*re(y)/ + \\1 + re (y) - im (y)/*\1 + re (y) - im (y) + cos(2*im(c))*e / + 2*\e *sin(2*im(c)) + 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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) - 2 \left(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \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(e^{2 \operatorname{re}{\left(c\right)}} \sin{\left(2 \operatorname{im}{\left(c\right)} \right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(e^{2 \operatorname{re}{\left(c\right)}} \cos{\left(2 \operatorname{im}{\left(c\right)} \right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)\right)^{2}} e^{i \operatorname{atan_{2}}{\left(- \frac{\left(\frac{i \left(e^{4 i \operatorname{im}{\left(c\right)}} - 1\right) e^{- 2 i \operatorname{im}{\left(c\right)}} \left(\operatorname{re}{\left(y\right)}\right)^{2}}{2} - \frac{i \left(e^{4 i \operatorname{im}{\left(c\right)}} - 1\right) e^{- 2 i \operatorname{im}{\left(c\right)}} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{2} + \frac{i \left(e^{4 i \operatorname{im}{\left(c\right)}} - 1\right) e^{- 2 i \operatorname{im}{\left(c\right)}}}{2} + \left(e^{4 i \operatorname{im}{\left(c\right)}} + 1\right) e^{- 2 i \operatorname{im}{\left(c\right)}} \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) e^{2 \operatorname{re}{\left(c\right)}}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4} - 2 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1},\frac{- 2 \left(\frac{i \left(e^{4 i \operatorname{im}{\left(c\right)}} - 1\right) e^{- 2 i \operatorname{im}{\left(c\right)}} e^{2 \operatorname{re}{\left(c\right)}}}{2} - 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\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(\frac{\left(e^{4 i \operatorname{im}{\left(c\right)}} + 1\right) e^{- 2 i \operatorname{im}{\left(c\right)}} e^{2 \operatorname{re}{\left(c\right)}}}{2} + \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}} \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(((exp(2*re(c))*sin(2*im(c)) + 2*im(y)*re(y))*(1 + re(y)^2 - im(y)^2) - 2*(1 + re(y)^2 - im(y)^2 + cos(2*im(c))*exp(2*re(c)))*im(y)*re(y))^2 + ((1 + re(y)^2 - im(y)^2)*(1 + re(y)^2 - im(y)^2 + cos(2*im(c))*exp(2*re(c))) + 2*(exp(2*re(c))*sin(2*im(c)) + 2*im(y)*re(y))*im(y)*re(y))^2)*exp(i*atan2(-(i*(-1 + exp(4*i*im(c)))*exp(-2*i*im(c))/2 + (1 + exp(4*i*im(c)))*exp(-2*i*im(c))*im(y)*re(y) + i*re(y)^2*(-1 + exp(4*i*im(c)))*exp(-2*i*im(c))/2 - i*im(y)^2*(-1 + exp(4*i*im(c)))*exp(-2*i*im(c))/2)*exp(2*re(c))/(1 + im(y)^4 + re(y)^4 - 2*im(y)^2 + 2*re(y)^2 + 2*im(y)^2*re(y)^2), ((1 + re(y)^2 - im(y)^2)*(1 + re(y)^2 - im(y)^2 + (1 + exp(4*i*im(c)))*exp(2*re(c))*exp(-2*i*im(c))/2) - 2*(-2*im(y)*re(y) + i*(-1 + exp(4*i*im(c)))*exp(2*re(c))*exp(-2*i*im(c))/2)*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)