Sr Examen
Otras calculadoras
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¿Cómo usar?
- La ecuación:
-
Ecuación 2+x=6
-
Ecuación 53x^2=0
-
Ecuación (x+3)/(x-3)=(2*x+3)/x
- Ecuación 5*x+3*y=4
- Expresar {x} en función de y en la ecuación:
- 9*x+7*y=4
- -4*x+18*y=-6
- -10*x+15*y=-19
- 18*x-7*y=-13
-
Expresiones idénticas
- x×(y^ seis + uno)×d×x+y^ dos ×(x^ cuatro + uno)×d×y= cero
- x×(y en el grado 6 más 1)×d×x más y al cuadrado ×(x en el grado 4 más 1)×d×y es igual a 0
- x×(y en el grado seis más uno)×d×x más y en el grado dos ×(x en el grado cuatro más uno)×d×y es igual a cero
- x×(y6+1)×d×x+y2×(x4+1)×d×y=0
- x×y6+1×d×x+y2×x4+1×d×y=0
- x×(y⁶+1)×d×x+y²×(x⁴+1)×d×y=0
- x×(y en el grado 6+1)×d×x+y en el grado 2×(x en el grado 4+1)×d×y=0
- x×y^6+1×d×x+y^2×x^4+1×d×y=0
- x×(y^6+1)×d×x+y^2×(x^4+1)×d×y=O
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Expresiones semejantes
- x×(y^6-1)×d×x+y^2×(x^4+1)×d×y=0
- x×(y^6+1)×d×x+y^2×(x^4-1)×d×y=0
- x×(y^6+1)×d×x-y^2×(x^4+1)×d×y=0
x×(y^6+1)×d×x+y^2×(x^4+1)×d×y=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 6 \ 2 / 4 \ x*\y + 1/*d*x + y *\x + 1/*d*y = 0
$$x d x \left(y^{6} + 1\right) + y d y^{2} \left(x^{4} + 1\right) = 0$$
Gráfica
Respuesta rápida
[src]
/ / 2 2 \\ / / 2 2 \\
| | 2*im(x)*re(x) im (x) re (x) || | | 2*im(x)*re(x) im (x) re (x) ||
_________________________________________________________________ |atan2|------------------, ------------------ - ------------------|| _________________________________________________________________ |atan2|------------------, ------------------ - ------------------||
/ 2 | | 2 2 2|| / 2 | | 2 2 2||
/ / 2 2 \ 2 2 | |/ 2 2 \ / 2 2 \ / 2 2 \ || / / 2 2 \ 2 2 | |/ 2 2 \ / 2 2 \ / 2 2 \ ||
/ | im (x) re (x) | 4*im (x)*re (x) | \\im (x) + re (x)/ \im (x) + re (x)/ \im (x) + re (x)/ /| / | im (x) re (x) | 4*im (x)*re (x) | \\im (x) + re (x)/ \im (x) + re (x)/ \im (x) + re (x)/ /|
y1 = / |------------------ - ------------------| + ------------------ *cos|------------------------------------------------------------------| + I* / |------------------ - ------------------| + ------------------ *sin|------------------------------------------------------------------|
/ | 2 2| 4 \ 3 / / | 2 2| 4 \ 3 /
6 / |/ 2 2 \ / 2 2 \ | / 2 2 \ 6 / |/ 2 2 \ / 2 2 \ | / 2 2 \
\/ \\im (x) + re (x)/ \im (x) + re (x)/ / \im (x) + re (x)/ \/ \\im (x) + re (x)/ \im (x) + re (x)/ / \im (x) + re (x)/
$$y_{1} = i \sqrt[6]{\left(- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}},- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)} + \sqrt[6]{\left(- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}},- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}$$
______________________________________ ______________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\
6 / / 2 2 \ 2 2 |atan2\-2*im(x)*re(x), im (x) - re (x)/| 6 / / 2 2 \ 2 2 |atan2\-2*im(x)*re(x), im (x) - re (x)/|
y2 = \/ \im (x) - re (x)/ + 4*im (x)*re (x) *cos|--------------------------------------| + I*\/ \im (x) - re (x)/ + 4*im (x)*re (x) *sin|--------------------------------------|
\ 3 / \ 3 /
$$y_{2} = i \sqrt[6]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{3} \right)} + \sqrt[6]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{3} \right)}$$
/ / / 2 2 \\ / / 2 2 \\\ / / 2 2 \\ / / 2 2 \\
| | | 2*im(x)*re(x) im (x) re (x) || | | 2*im(x)*re(x) im (x) re (x) ||| | | 2*im(x)*re(x) im (x) re (x) || | | 2*im(x)*re(x) im (x) re (x) ||
| _________________________________________________________________ |atan2|------------------, ------------------ - ------------------|| _________________________________________________________________ |atan2|------------------, ------------------ - ------------------||| _________________________________________________________________ |atan2|------------------, ------------------ - ------------------|| _________________________________________________________________ |atan2|------------------, ------------------ - ------------------||
| / 2 | | 2 2 2|| / 2 | | 2 2 2||| / 2 | | 2 2 2|| / 2 | | 2 2 2||
| / / 2 2 \ 2 2 | |/ 2 2 \ / 2 2 \ / 2 2 \ || / / 2 2 \ 2 2 | |/ 2 2 \ / 2 2 \ / 2 2 \ ||| / / 2 2 \ 2 2 | |/ 2 2 \ / 2 2 \ / 2 2 \ || / / 2 2 \ 2 2 | |/ 2 2 \ / 2 2 \ / 2 2 \ ||
| / | im (x) re (x) | 4*im (x)*re (x) | \\im (x) + re (x)/ \im (x) + re (x)/ \im (x) + re (x)/ /| ___ / | im (x) re (x) | 4*im (x)*re (x) | \\im (x) + re (x)/ \im (x) + re (x)/ \im (x) + re (x)/ /|| / | im (x) re (x) | 4*im (x)*re (x) | \\im (x) + re (x)/ \im (x) + re (x)/ \im (x) + re (x)/ /| ___ / | im (x) re (x) | 4*im (x)*re (x) | \\im (x) + re (x)/ \im (x) + re (x)/ \im (x) + re (x)/ /|
| / |------------------ - ------------------| + ------------------ *sin|------------------------------------------------------------------| \/ 3 * / |------------------ - ------------------| + ------------------ *cos|------------------------------------------------------------------|| / |------------------ - ------------------| + ------------------ *cos|------------------------------------------------------------------| \/ 3 * / |------------------ - ------------------| + ------------------ *sin|------------------------------------------------------------------|
| / | 2 2| 4 \ 3 / / | 2 2| 4 \ 3 /| / | 2 2| 4 \ 3 / / | 2 2| 4 \ 3 /
| 6 / |/ 2 2 \ / 2 2 \ | / 2 2 \ 6 / |/ 2 2 \ / 2 2 \ | / 2 2 \ | 6 / |/ 2 2 \ / 2 2 \ | / 2 2 \ 6 / |/ 2 2 \ / 2 2 \ | / 2 2 \
| \/ \\im (x) + re (x)/ \im (x) + re (x)/ / \im (x) + re (x)/ \/ \\im (x) + re (x)/ \im (x) + re (x)/ / \im (x) + re (x)/ | \/ \\im (x) + re (x)/ \im (x) + re (x)/ / \im (x) + re (x)/ \/ \\im (x) + re (x)/ \im (x) + re (x)/ / \im (x) + re (x)/
y3 = I*|- ------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------
\ 2 2 / 2 2
$$y_{3} = i \left(- \frac{\sqrt[6]{\left(- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}},- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sqrt[6]{\left(- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}},- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}\right) + \frac{\sqrt{3} \sqrt[6]{\left(- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}},- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}},- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}$$
/ / / 2 2 \\ / / 2 2 \\\ / / 2 2 \\ / / 2 2 \\
| | | 2*im(x)*re(x) im (x) re (x) || | | 2*im(x)*re(x) im (x) re (x) ||| | | 2*im(x)*re(x) im (x) re (x) || | | 2*im(x)*re(x) im (x) re (x) ||
| _________________________________________________________________ |atan2|------------------, ------------------ - ------------------|| _________________________________________________________________ |atan2|------------------, ------------------ - ------------------||| _________________________________________________________________ |atan2|------------------, ------------------ - ------------------|| _________________________________________________________________ |atan2|------------------, ------------------ - ------------------||
| / 2 | | 2 2 2|| / 2 | | 2 2 2||| / 2 | | 2 2 2|| / 2 | | 2 2 2||
| / / 2 2 \ 2 2 | |/ 2 2 \ / 2 2 \ / 2 2 \ || / / 2 2 \ 2 2 | |/ 2 2 \ / 2 2 \ / 2 2 \ ||| / / 2 2 \ 2 2 | |/ 2 2 \ / 2 2 \ / 2 2 \ || / / 2 2 \ 2 2 | |/ 2 2 \ / 2 2 \ / 2 2 \ ||
| / | im (x) re (x) | 4*im (x)*re (x) | \\im (x) + re (x)/ \im (x) + re (x)/ \im (x) + re (x)/ /| ___ / | im (x) re (x) | 4*im (x)*re (x) | \\im (x) + re (x)/ \im (x) + re (x)/ \im (x) + re (x)/ /|| / | im (x) re (x) | 4*im (x)*re (x) | \\im (x) + re (x)/ \im (x) + re (x)/ \im (x) + re (x)/ /| ___ / | im (x) re (x) | 4*im (x)*re (x) | \\im (x) + re (x)/ \im (x) + re (x)/ \im (x) + re (x)/ /|
| / |------------------ - ------------------| + ------------------ *sin|------------------------------------------------------------------| \/ 3 * / |------------------ - ------------------| + ------------------ *cos|------------------------------------------------------------------|| / |------------------ - ------------------| + ------------------ *cos|------------------------------------------------------------------| \/ 3 * / |------------------ - ------------------| + ------------------ *sin|------------------------------------------------------------------|
| / | 2 2| 4 \ 3 / / | 2 2| 4 \ 3 /| / | 2 2| 4 \ 3 / / | 2 2| 4 \ 3 /
| 6 / |/ 2 2 \ / 2 2 \ | / 2 2 \ 6 / |/ 2 2 \ / 2 2 \ | / 2 2 \ | 6 / |/ 2 2 \ / 2 2 \ | / 2 2 \ 6 / |/ 2 2 \ / 2 2 \ | / 2 2 \
| \/ \\im (x) + re (x)/ \im (x) + re (x)/ / \im (x) + re (x)/ \/ \\im (x) + re (x)/ \im (x) + re (x)/ / \im (x) + re (x)/ | \/ \\im (x) + re (x)/ \im (x) + re (x)/ / \im (x) + re (x)/ \/ \\im (x) + re (x)/ \im (x) + re (x)/ / \im (x) + re (x)/
y4 = I*|- ------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------
\ 2 2 / 2 2
$$y_{4} = i \left(- \frac{\sqrt[6]{\left(- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}},- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} + \frac{\sqrt{3} \sqrt[6]{\left(- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}},- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}\right) - \frac{\sqrt{3} \sqrt[6]{\left(- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}},- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}},- \frac{\left(\operatorname{re}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}$$
/ ______________________________________ ______________________________________ \ ______________________________________ ______________________________________
| / 2 / / 2 2 \\ / 2 / / 2 2 \\| / 2 / / 2 2 \\ / 2 / / 2 2 \\
| 6 / / 2 2 \ 2 2 |atan2\-2*im(x)*re(x), im (x) - re (x)/| ___ 6 / / 2 2 \ 2 2 |atan2\-2*im(x)*re(x), im (x) - re (x)/|| 6 / / 2 2 \ 2 2 |atan2\-2*im(x)*re(x), im (x) - re (x)/| ___ 6 / / 2 2 \ 2 2 |atan2\-2*im(x)*re(x), im (x) - re (x)/|
| \/ \im (x) - re (x)/ + 4*im (x)*re (x) *sin|--------------------------------------| \/ 3 *\/ \im (x) - re (x)/ + 4*im (x)*re (x) *cos|--------------------------------------|| \/ \im (x) - re (x)/ + 4*im (x)*re (x) *cos|--------------------------------------| \/ 3 *\/ \im (x) - re (x)/ + 4*im (x)*re (x) *sin|--------------------------------------|
| \ 3 / \ 3 /| \ 3 / \ 3 /
y5 = I*|- -------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------| - -------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------
\ 2 2 / 2 2
$$y_{5} = i \left(- \frac{\sqrt[6]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sqrt[6]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{3} \right)}}{2}\right) + \frac{\sqrt{3} \sqrt[6]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{3} \right)}}{2}$$
/ ______________________________________ ______________________________________ \ ______________________________________ ______________________________________
| / 2 / / 2 2 \\ / 2 / / 2 2 \\| / 2 / / 2 2 \\ / 2 / / 2 2 \\
| 6 / / 2 2 \ 2 2 |atan2\-2*im(x)*re(x), im (x) - re (x)/| ___ 6 / / 2 2 \ 2 2 |atan2\-2*im(x)*re(x), im (x) - re (x)/|| 6 / / 2 2 \ 2 2 |atan2\-2*im(x)*re(x), im (x) - re (x)/| ___ 6 / / 2 2 \ 2 2 |atan2\-2*im(x)*re(x), im (x) - re (x)/|
| \/ \im (x) - re (x)/ + 4*im (x)*re (x) *sin|--------------------------------------| \/ 3 *\/ \im (x) - re (x)/ + 4*im (x)*re (x) *cos|--------------------------------------|| \/ \im (x) - re (x)/ + 4*im (x)*re (x) *cos|--------------------------------------| \/ 3 *\/ \im (x) - re (x)/ + 4*im (x)*re (x) *sin|--------------------------------------|
| \ 3 / \ 3 /| \ 3 / \ 3 /
y6 = I*|- -------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------| - -------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------
\ 2 2 / 2 2
$$y_{6} = i \left(- \frac{\sqrt[6]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{3} \right)}}{2} + \frac{\sqrt{3} \sqrt[6]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{3} \right)}}{2}\right) - \frac{\sqrt{3} \sqrt[6]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},- \left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2} \right)}}{3} \right)}}{2}$$
y6 = i*(-((-re(x)^2 + im(x)^2)^2 + 4*re(x)^2*im(x)^2)^(1/6)*sin(atan2(-2*re(x)*im(x, -re(x)^2 + im(x)^2)/3)/2 + sqrt(3)*((-re(x)^2 + im(x)^2)^2 + 4*re(x)^2*im(x)^2)^(1/6)*cos(atan2(-2*re(x)*im(x), -re(x)^2 + im(x)^2)/3)/2) - sqrt(3)*((-re(x)^2 + im(x)^2)^2 + 4*re(x)^2*im(x)^2)^(1/6)*sin(atan2(-2*re(x)*im(x), -re(x)^2 + im(x)^2)/3)/2 - ((-re(x)^2 + im(x)^2)^2 + 4*re(x)^2*im(x)^2)^(1/6)*cos(atan2(-2*re(x)*im(x), -re(x)^2 + im(x)^2)/3)/2)