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Ecuación 8*x-3*(2*x+1)=2*x+4
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Ecuación x^3=27
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Ecuación 1+sin(x)=0
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Ecuación 2*x^2+6*x+9=
- Expresar {x} en función de y en la ecuación:
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Expresiones idénticas
- y*x.diff(x)+x=(cuatro *y^ tres)+(tres *y^ dos)
- y multiplicar por x.diff(x) más x es igual a (4 multiplicar por y al cubo ) más (3 multiplicar por y al cuadrado )
- y multiplicar por x.diff(x) más x es igual a (cuatro multiplicar por y en el grado tres) más (tres multiplicar por y en el grado dos)
- y*x.diff(x)+x=(4*y3)+(3*y2)
- y*x.diffx+x=4*y3+3*y2
- y*x.diff(x)+x=(4*y³)+(3*y²)
- y*x.diff(x)+x=(4*y en el grado 3)+(3*y en el grado 2)
- yx.diff(x)+x=(4y^3)+(3y^2)
- yx.diff(x)+x=(4y3)+(3y2)
- yx.diffx+x=4y3+3y2
- yx.diffx+x=4y^3+3y^2
-
Expresiones semejantes
- y*x.diff(x)+x=(4*y^3)-(3*y^2)
- y*x.diff(x)-x=(4*y^3)+(3*y^2)
y*x.diff(x)+x=(4*y^3)+(3*y^2) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
//x for 0 = 1\ || | 3 2 y*|<1 for 1 = 1| + x = 4*y + 3*y || | \\0 otherwise/
$$x + y \left(\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases}\right) = 4 y^{3} + 3 y^{2}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$x + y \left(\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases}\right) = 4 y^{3} + 3 y^{2}$$
de
$$a y^{3} + b y^{2} + c y + d = 0$$
como ecuación cúbica reducida
$$y^{3} + \frac{b y^{2}}{a} + \frac{c y}{a} + \frac{d}{a} = 0$$
$$- \frac{x}{4} + y^{3} + \frac{3 y^{2}}{4} - \frac{y}{4} = 0$$
$$p y^{2} + q y + v + y^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{3}{4}$$
$$q = \frac{c}{a}$$
$$q = - \frac{\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases}}{4}$$
$$v = \frac{d}{a}$$
$$v = - \frac{x}{4}$$
Fórmulas de Cardano-Vieta
$$y_{1} + y_{2} + y_{3} = - p$$
$$y_{1} y_{2} + y_{1} y_{3} + y_{2} y_{3} = q$$
$$y_{1} y_{2} y_{3} = v$$
$$y_{1} + y_{2} + y_{3} = - \frac{3}{4}$$
$$y_{1} y_{2} + y_{1} y_{3} + y_{2} y_{3} = - \frac{\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases}}{4}$$
$$y_{1} y_{2} y_{3} = - \frac{x}{4}$$
$$x + y \left(\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases}\right) = 4 y^{3} + 3 y^{2}$$
de
$$a y^{3} + b y^{2} + c y + d = 0$$
como ecuación cúbica reducida
$$y^{3} + \frac{b y^{2}}{a} + \frac{c y}{a} + \frac{d}{a} = 0$$
$$- \frac{x}{4} + y^{3} + \frac{3 y^{2}}{4} - \frac{y}{4} = 0$$
$$p y^{2} + q y + v + y^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{3}{4}$$
$$q = \frac{c}{a}$$
$$q = - \frac{\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases}}{4}$$
$$v = \frac{d}{a}$$
$$v = - \frac{x}{4}$$
Fórmulas de Cardano-Vieta
$$y_{1} + y_{2} + y_{3} = - p$$
$$y_{1} y_{2} + y_{1} y_{3} + y_{2} y_{3} = q$$
$$y_{1} y_{2} y_{3} = v$$
$$y_{1} + y_{2} + y_{3} = - \frac{3}{4}$$
$$y_{1} y_{2} + y_{1} y_{3} + y_{2} y_{3} = - \frac{\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases}}{4}$$
$$y_{1} y_{2} y_{3} = - \frac{x}{4}$$
Gráfica
Respuesta rápida
[src]
/ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _________________________________________________________________________ / / /81 27*re(x)\ \\ _________________________________________________________________________ / / /81 27*re(x)\ \\\\ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _________________________________________________________________________ / / /81 27*re(x)\ \\ _________________________________________________________________________ / / /81 27*re(x)\ \\\\\ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _________________________________________________________________________ / / /81 27*re(x)\ \\ _________________________________________________________________________ / / /81 27*re(x)\ \\\\ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _________________________________________________________________________ / / /81 27*re(x)\ \\ _________________________________________________________________________ / / /81 27*re(x)\ \\\\
/ 1 \ | / 1 \ / 2 2 | | / 2 | |-27*|-- - --------|*im(x) 2 2 || / 2 | |-27*|-- - --------|*im(x) 2 2 |||| / 2 2 | | / 2 | |-27*|-- - --------|*im(x) 2 2 || / 2 | |-27*|-- - --------|*im(x) 2 2 ||||| / 2 2 | | / 2 | |-27*|-- - --------|*im(x) 2 2 || / 2 | |-27*|-- - --------|*im(x) 2 2 |||| / 2 2 | | / 2 | |-27*|-- - --------|*im(x) 2 2 || / 2 | |-27*|-- - --------|*im(x) 2 2 ||||
7*re|------------------------------------------------------------------| | 7*im|------------------------------------------------------------------| / / _________________________________________________________________________ / / /81 27*re(x)\ \\\ / _________________________________________________________________________ / / /81 27*re(x)\ \\\ | | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|| / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|||| / / _________________________________________________________________________ / / /81 27*re(x)\ \\\ / _________________________________________________________________________ / / /81 27*re(x)\ \\\ | | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|| / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||||| / / _________________________________________________________________________ / / /81 27*re(x)\ \\\ / _________________________________________________________________________ / / /81 27*re(x)\ \\\ | | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|| / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|||| / / _________________________________________________________________________ / / /81 27*re(x)\ \\\ / _________________________________________________________________________ / / /81 27*re(x)\ \\\ | | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|| / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||||
| __________________________________________| | | __________________________________________| / | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|| / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|||| / | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|| / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||||| / | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|| / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|||| / | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|| / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||||
| / _______________________ | | | / _______________________ | / | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /| / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /||| / | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /| / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|||| / | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /| / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /||| / | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /| / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|||
| / / 2 | | | / / 2 | / | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------| 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------||| / | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------| 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|||| / | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------| 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------||| / | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------| 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|||
| / / 9261 /81 27*x\ | | | / / 9261 /81 27*x\ | / | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 / 81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /|| / | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 / 81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /||| / | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 / 81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /|| / | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 / 81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /||
|/ ___\ / / - ---- + |-- - ----| | | |/ ___\ / / - ---- + |-- - ----| | / | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------|| | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|| |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------, -- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------|| / | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------|| | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|| |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------, -- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------||| / | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------|| | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|| |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------, -- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------|| / | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------|| | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|| |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------, -- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------||
|| 1 I*\/ 3 | / 81 \/ 1024 \32 4 / 27*x | | || 1 I*\/ 3 | / 81 \/ 1024 \32 4 / 27*x | / | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| |81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| | \ 8 2 64 8 2 /| ___ / | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| |81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| | \ 8 2 64 8 2 /|| / | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| |81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| | \ 8 2 64 8 2 /| ___ / | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| |81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| | \ 8 2 64 8 2 /|
||- - - -------|*3 / -- + ---------------------------- - ---- | | ||- - - -------|*3 / -- + ---------------------------- - ---- | 6 / |- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| 6 / |- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
1 \\ 2 2 / \/ 64 2 8 / | \\ 2 2 / \/ 64 2 8 / \/ \ 8 2 / \64 8 2 / \ 3 / \/ \ 8 2 / \64 8 2 / \ 3 /| \/ \ 8 2 / \64 8 2 / \ 3 / \/ \ 8 2 / \64 8 2 / \ 3 /
y1 = - - - ------------------------------------------------------------------------ + I*|- ------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4 16 \ 16 6 6 / 6 6
$$y_{1} = - \frac{\sqrt{3} \sqrt[6]{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8}\right)^{2} + \left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8},\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64} \right)}}{3} \right)}}{6} + \frac{\sqrt[6]{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8}\right)^{2} + \left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8},\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64} \right)}}{3} \right)}}{6} + i \left(\frac{\sqrt[6]{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8}\right)^{2} + \left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8},\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64} \right)}}{3} \right)}}{6} + \frac{\sqrt{3} \sqrt[6]{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8}\right)^{2} + \left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8},\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64} \right)}}{3} \right)}}{6} - \frac{7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 x}{8} + \frac{\sqrt{\left(\frac{81}{32} - \frac{27 x}{4}\right)^{2} - \frac{9261}{1024}}}{2} + \frac{81}{64}}}\right)}}{16}\right) - \frac{7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 x}{8} + \frac{\sqrt{\left(\frac{81}{32} - \frac{27 x}{4}\right)^{2} - \frac{9261}{1024}}}{2} + \frac{81}{64}}}\right)}}{16} - \frac{1}{4}$$
/ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _________________________________________________________________________ / / /81 27*re(x)\ \\ _________________________________________________________________________ / / /81 27*re(x)\ \\\\ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _________________________________________________________________________ / / /81 27*re(x)\ \\ _________________________________________________________________________ / / /81 27*re(x)\ \\\\\ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _________________________________________________________________________ / / /81 27*re(x)\ \\ _________________________________________________________________________ / / /81 27*re(x)\ \\\\ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _________________________________________________________________________ / / /81 27*re(x)\ \\ _________________________________________________________________________ / / /81 27*re(x)\ \\\\
/ 1 \ | / 1 \ / 2 2 | | / 2 | |-27*|-- - --------|*im(x) 2 2 || / 2 | |-27*|-- - --------|*im(x) 2 2 |||| / 2 2 | | / 2 | |-27*|-- - --------|*im(x) 2 2 || / 2 | |-27*|-- - --------|*im(x) 2 2 ||||| / 2 2 | | / 2 | |-27*|-- - --------|*im(x) 2 2 || / 2 | |-27*|-- - --------|*im(x) 2 2 |||| / 2 2 | | / 2 | |-27*|-- - --------|*im(x) 2 2 || / 2 | |-27*|-- - --------|*im(x) 2 2 ||||
7*re|------------------------------------------------------------------| | 7*im|------------------------------------------------------------------| / / _________________________________________________________________________ / / /81 27*re(x)\ \\\ / _________________________________________________________________________ / / /81 27*re(x)\ \\\ | | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|| / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|||| / / _________________________________________________________________________ / / /81 27*re(x)\ \\\ / _________________________________________________________________________ / / /81 27*re(x)\ \\\ | | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|| / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||||| / / _________________________________________________________________________ / / /81 27*re(x)\ \\\ / _________________________________________________________________________ / / /81 27*re(x)\ \\\ | | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|| / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|||| / / _________________________________________________________________________ / / /81 27*re(x)\ \\\ / _________________________________________________________________________ / / /81 27*re(x)\ \\\ | | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|| / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||||
| __________________________________________| | | __________________________________________| / | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|| / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|||| / | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|| / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||||| / | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|| / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|||| / | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|| / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||||
| / _______________________ | | | / _______________________ | / | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /| / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /||| / | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /| / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|||| / | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /| / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /||| / | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /| / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|||
| / / 2 | | | / / 2 | / | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------| 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------||| / | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------| 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|||| / | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------| 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------||| / | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------| 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|||
| / / 9261 /81 27*x\ | | | / / 9261 /81 27*x\ | / | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 / 81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /|| / | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 / 81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /||| / | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 / 81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /|| / | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 / 81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /||
|/ ___\ / / - ---- + |-- - ----| | | |/ ___\ / / - ---- + |-- - ----| | / | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------|| | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|| |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------, -- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------|| / | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------|| | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|| |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------, -- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------||| / | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------|| | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|| |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------, -- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------|| / | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------|| | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|| |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------, -- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------||
|| 1 I*\/ 3 | / 81 \/ 1024 \32 4 / 27*x | | || 1 I*\/ 3 | / 81 \/ 1024 \32 4 / 27*x | / | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| |81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| | \ 8 2 64 8 2 /| ___ / | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| |81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| | \ 8 2 64 8 2 /|| / | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| |81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| | \ 8 2 64 8 2 /| ___ / | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| |81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| | \ 8 2 64 8 2 /|
||- - + -------|*3 / -- + ---------------------------- - ---- | | ||- - + -------|*3 / -- + ---------------------------- - ---- | 6 / |- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| 6 / |- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
1 \\ 2 2 / \/ 64 2 8 / | \\ 2 2 / \/ 64 2 8 / \/ \ 8 2 / \64 8 2 / \ 3 / \/ \ 8 2 / \64 8 2 / \ 3 /| \/ \ 8 2 / \64 8 2 / \ 3 / \/ \ 8 2 / \64 8 2 / \ 3 /
y2 = - - - ------------------------------------------------------------------------ + I*|- ------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4 16 \ 16 6 6 / 6 6
$$y_{2} = \frac{\sqrt{3} \sqrt[6]{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8}\right)^{2} + \left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8},\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64} \right)}}{3} \right)}}{6} + \frac{\sqrt[6]{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8}\right)^{2} + \left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8},\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64} \right)}}{3} \right)}}{6} + i \left(\frac{\sqrt[6]{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8}\right)^{2} + \left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8},\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64} \right)}}{3} \right)}}{6} - \frac{\sqrt{3} \sqrt[6]{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8}\right)^{2} + \left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8},\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64} \right)}}{3} \right)}}{6} - \frac{7 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 x}{8} + \frac{\sqrt{\left(\frac{81}{32} - \frac{27 x}{4}\right)^{2} - \frac{9261}{1024}}}{2} + \frac{81}{64}}}\right)}}{16}\right) - \frac{7 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{27 x}{8} + \frac{\sqrt{\left(\frac{81}{32} - \frac{27 x}{4}\right)^{2} - \frac{9261}{1024}}}{2} + \frac{81}{64}}}\right)}}{16} - \frac{1}{4}$$
/ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _________________________________________________________________________ / / /81 27*re(x)\ \\ _________________________________________________________________________ / / /81 27*re(x)\ \\\\ / / _________________________________________________________________________ / / /81 27*re(x)\ \\ _________________________________________________________________________ / / /81 27*re(x)\ \\\\ \ / / _________________________________________________________________________ / / /81 27*re(x)\ \\ _________________________________________________________________________ / / /81 27*re(x)\ \\\\ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _________________________________________________________________________ / / /81 27*re(x)\ \\ _________________________________________________________________________ / / /81 27*re(x)\ \\\\
| / 2 2 | | / 2 | |-27*|-- - --------|*im(x) 2 2 || / 2 | |-27*|-- - --------|*im(x) 2 2 |||| | | / 2 | |-27*|-- - --------|*im(x) 2 2 || / 2 | |-27*|-- - --------|*im(x) 2 2 |||| | | | / 2 | |-27*|-- - --------|*im(x) 2 2 || / 2 | |-27*|-- - --------|*im(x) 2 2 |||| / 2 2 | | / 2 | |-27*|-- - --------|*im(x) 2 2 || / 2 | |-27*|-- - --------|*im(x) 2 2 ||||
| / / _________________________________________________________________________ / / /81 27*re(x)\ \\\ / _________________________________________________________________________ / / /81 27*re(x)\ \\\ | | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|| / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|||| | | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|| / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|||| | | | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|| / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|||| / / _________________________________________________________________________ / / /81 27*re(x)\ \\\ / _________________________________________________________________________ / / /81 27*re(x)\ \\\ | | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|| / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||||
| / | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|| / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|||| | | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|| / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|||| | | | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|| / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|||| / | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|| / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||||
| / | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /| / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /||| | | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /| / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /||| | | | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /| / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /||| / | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /| / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|||
| / | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------| 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------||| | | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------| 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------||| | | | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------| 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------||| / | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------| 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|||
| / | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 / 81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /|| | | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 / 81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /|| | | | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 / 81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /|| / | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 / 81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /||
| / | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------|| | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|| |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------, -- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------|| |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------, -- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------|| | |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------, -- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------|| / | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------|| | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|| |atan2|- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------, -- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------||
| / | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| |81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| | \ 8 2 64 8 2 /| | \ 8 2 64 8 2 /| | | \ 8 2 64 8 2 /| / | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| |81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| | \ 8 2 64 8 2 /|
| 6 / |- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| 7*sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | 7*cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| 6 / |- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
1 | \/ \ 8 2 / \64 8 2 / \ 3 / \ 3 / | \ 3 / \/ \ 8 2 / \64 8 2 / \ 3 /
y3 = - - + I*|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4 | 3 ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________| ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 3
| / 2 2 | / 2 2
| / / _________________________________________________________________________ / / /81 27*re(x)\ \\\ / _________________________________________________________________________ / / /81 27*re(x)\ \\\ | / / _________________________________________________________________________ / / /81 27*re(x)\ \\\ / _________________________________________________________________________ / / /81 27*re(x)\ \\\
| / | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | / | / 2 | |-27*|-- - --------|*im(x) 2 2 ||| | / 2 | |-27*|-- - --------|*im(x) 2 2 |||
| / | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | / | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)||| | / 2 /81 27*re(x)\ 2 | | \32 4 / 9261 /81 27*re(x)\ 729*im (x)|||
| / | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | / | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------||| | / / 2 2 \ 729*|-- - --------| *im (x) |atan2|-------------------------, - ---- + |-- - --------| - ----------|||
| / | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | / | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /|| | / | 9261 /81 27*re(x)\ 729*im (x)| \32 4 / | \ 2 1024 \32 4 / 16 /||
| / | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------|| | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------|| | / | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *sin|------------------------------------------------------------------------|| | 4 / |- ---- + |-- - --------| - ----------| + --------------------------- *cos|------------------------------------------------------------------------||
| / | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| |81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| | / | 27*im(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /| |81 27*re(x) \/ \ 1024 \32 4 / 16 / 4 \ 2 /|
| 16*6 / |- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| | 16*6 / |- -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-- - -------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------|
\ \/ \ 8 2 / \64 8 2 / / \/ \ 8 2 / \64 8 2 /
$$y_{3} = i \left(- \frac{\sqrt[6]{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8}\right)^{2} + \left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8},\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64} \right)}}{3} \right)}}{3} + \frac{7 \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8},\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64} \right)}}{3} \right)}}{16 \sqrt[6]{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8}\right)^{2} + \left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64}\right)^{2}}}\right) - \frac{\sqrt[6]{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8}\right)^{2} + \left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8},\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64} \right)}}{3} \right)}}{3} - \frac{1}{4} - \frac{7 \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8},\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64} \right)}}{3} \right)}}{16 \sqrt[6]{\left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{im}{\left(x\right)}}{8}\right)^{2} + \left(\frac{\sqrt[4]{\frac{729 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{4} + \left(\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{27 \left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right) \operatorname{im}{\left(x\right)}}{2},\left(\frac{81}{32} - \frac{27 \operatorname{re}{\left(x\right)}}{4}\right)^{2} - \frac{729 \left(\operatorname{im}{\left(x\right)}\right)^{2}}{16} - \frac{9261}{1024} \right)}}{2} \right)}}{2} - \frac{27 \operatorname{re}{\left(x\right)}}{8} + \frac{81}{64}\right)^{2}}}$$
y3 = i*(-(((729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*sin(atan2(-27*(81/32 - 27*re(x)/4)*im(x/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*im(x)/8)^2 + ((729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*cos(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*re(x)/8 + 81/64)^2)^(1/6)*sin(atan2((729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*sin(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*im(x)/8, (729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*cos(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*re(x)/8 + 81/64)/3)/3 + 7*sin(atan2((729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*sin(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*im(x)/8, (729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*cos(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*re(x)/8 + 81/64)/3)/(16*(((729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*sin(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*im(x)/8)^2 + ((729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*cos(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*re(x)/8 + 81/64)^2)^(1/6))) - (((729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*sin(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*im(x)/8)^2 + ((729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*cos(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*re(x)/8 + 81/64)^2)^(1/6)*cos(atan2((729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*sin(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*im(x)/8, (729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*cos(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*re(x)/8 + 81/64)/3)/3 - 1/4 - 7*cos(atan2((729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*sin(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*im(x)/8, (729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*cos(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*re(x)/8 + 81/64)/3)/(16*(((729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*sin(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*im(x)/8)^2 + ((729*(81/32 - 27*re(x)/4)^2*im(x)^2/4 + ((81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)^2)^(1/4)*cos(atan2(-27*(81/32 - 27*re(x)/4)*im(x)/2, (81/32 - 27*re(x)/4)^2 - 729*im(x)^2/16 - 9261/1024)/2)/2 - 27*re(x)/8 + 81/64)^2)^(1/6)))