Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación x+9=0
-
Ecuación 2x^2+7x-9=0
-
Ecuación 3,4+2y=7(y-2,3)
-
Ecuación 9x-4x+39=94
- Expresar {x} en función de y en la ecuación:
- -16*x+3*y=17
- 18*x-14*y=-2
- 18*x+19*y=10
- 11*x-6*y=5
-
Expresiones idénticas
- x= uno /(y^(uno / dos))+ uno /(y^(uno / tres))+ uno /(y^(uno / cuatro))
- x es igual a 1 dividir por (y en el grado (1 dividir por 2)) más 1 dividir por (y en el grado (1 dividir por 3)) más 1 dividir por (y en el grado (1 dividir por 4))
- x es igual a uno dividir por (y en el grado (uno dividir por dos)) más uno dividir por (y en el grado (uno dividir por tres)) más uno dividir por (y en el grado (uno dividir por cuatro))
- x=1/(y(1/2))+1/(y(1/3))+1/(y(1/4))
- x=1/y1/2+1/y1/3+1/y1/4
- x=1/y^1/2+1/y^1/3+1/y^1/4
- x=1 dividir por (y^(1 dividir por 2))+1 dividir por (y^(1 dividir por 3))+1 dividir por (y^(1 dividir por 4))
-
Expresiones semejantes
- x=1/(y^(1/2))-1/(y^(1/3))+1/(y^(1/4))
- x=1/(y^(1/2))+1/(y^(1/3))-1/(y^(1/4))
x=1/(y^(1/2))+1/(y^(1/3))+1/(y^(1/4)) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
1 1 1
x = ----- + ----- + -----
___ 3 ___ 4 ___
\/ y \/ y \/ y
$$x = \left(\frac{1}{\sqrt{y}} + \frac{1}{\sqrt[3]{y}}\right) + \frac{1}{\sqrt[4]{y}}$$
Solución detallada
Tenemos la ecuación:
$$x = \left(\frac{1}{\sqrt{y}} + \frac{1}{\sqrt[3]{y}}\right) + \frac{1}{\sqrt[4]{y}}$$
cambiamos:
$$x = \frac{y^{\frac{7}{12}} + y^{\frac{5}{6}} + y^{\frac{3}{4}}}{y^{\frac{13}{12}}}$$
Abrimos los paréntesis en el miembro derecho de la ecuación
Obtenemos la respuesta: x = (y^(3/4) + y^(5/6) + y^(7/12))/y^(13/12)
$$x = \left(\frac{1}{\sqrt{y}} + \frac{1}{\sqrt[3]{y}}\right) + \frac{1}{\sqrt[4]{y}}$$
cambiamos:
$$x = \frac{y^{\frac{7}{12}} + y^{\frac{5}{6}} + y^{\frac{3}{4}}}{y^{\frac{13}{12}}}$$
Abrimos los paréntesis en el miembro derecho de la ecuación
x = y+3/4 + y^5/6 + y^7/12)/y^13/12
Obtenemos la respuesta: x = (y^(3/4) + y^(5/6) + y^(7/12))/y^(13/12)
Gráfica
Suma y producto de raíces
[src]
suma
// 3/8 5/12 7/24 \ / 3/8 5/12 7/24 \ \ / 3/8 5/12 7/24 \ / 3/8 5/12 7/24 \ ||/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\ |/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\| |/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\ |/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\ ||\im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------||*cos|----------------------| |\im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------||*sin|----------------------|| |\im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------||*cos|----------------------| |\im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------||*sin|----------------------| |\ \ 4 / \ 6 / \ 12 // \ 12 / \ \ 4 / \ 6 / \ 12 // \ 12 /| \ \ 4 / \ 6 / \ 12 // \ 12 / \ \ 4 / \ 6 / \ 12 // \ 12 / I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 13 13 | 13 13 | -- -- | -- -- | 24 24 | 24 24 | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ \ \im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/ \im (y) + re (y)/
$$i \left(\frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \sin{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \sin{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \cos{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}} - \frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \cos{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \cos{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \sin{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}}\right) + \frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \sin{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \sin{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \sin{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}} + \frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \cos{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \cos{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \cos{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}}$$
=
// 3/8 5/12 7/24 \ / 3/8 5/12 7/24 \ \ / 3/8 5/12 7/24 \ / 3/8 5/12 7/24 \ ||/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\ |/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\| |/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\ |/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\ ||\im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------||*cos|----------------------| |\im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------||*sin|----------------------|| |\im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------||*cos|----------------------| |\im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------||*sin|----------------------| |\ \ 4 / \ 6 / \ 12 // \ 12 / \ \ 4 / \ 6 / \ 12 // \ 12 /| \ \ 4 / \ 6 / \ 12 // \ 12 / \ \ 4 / \ 6 / \ 12 // \ 12 / I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 13 13 | 13 13 | -- -- | -- -- | 24 24 | 24 24 | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ \ \im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/ \im (y) + re (y)/
$$i \left(\frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \sin{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \sin{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \cos{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}} - \frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \cos{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \cos{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \sin{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}}\right) + \frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \sin{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \sin{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \sin{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}} + \frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \cos{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \cos{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \cos{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}}$$
producto
// 3/8 5/12 7/24 \ / 3/8 5/12 7/24 \ \ / 3/8 5/12 7/24 \ / 3/8 5/12 7/24 \ ||/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\ |/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\| |/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\ |/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\ ||\im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------||*cos|----------------------| |\im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------||*sin|----------------------|| |\im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------||*cos|----------------------| |\im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------||*sin|----------------------| |\ \ 4 / \ 6 / \ 12 // \ 12 / \ \ 4 / \ 6 / \ 12 // \ 12 /| \ \ 4 / \ 6 / \ 12 // \ 12 / \ \ 4 / \ 6 / \ 12 // \ 12 / I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 13 13 | 13 13 | -- -- | -- -- | 24 24 | 24 24 | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ \ \im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/ \im (y) + re (y)/
$$i \left(\frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \sin{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \sin{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \cos{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}} - \frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \cos{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \cos{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \sin{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}}\right) + \frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \sin{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \sin{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \sin{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}} + \frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \cos{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \cos{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \cos{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}}$$
=
/atan2(im(y), re(y))\ /atan2(im(y), re(y))\ /atan2(im(y), re(y))\ /atan2(im(y), re(y))\ /atan2(im(y), re(y))\ /atan2(im(y), re(y))\
cos|-------------------| cos|-------------------| cos|-------------------| I*sin|-------------------| I*sin|-------------------| I*sin|-------------------|
\ 2 / \ 3 / \ 4 / \ 2 / \ 3 / \ 4 /
------------------------ + ------------------------ + ------------------------ - -------------------------- - -------------------------- - --------------------------
_________________ _________________ _________________ _________________ _________________ _________________
4 / 2 2 6 / 2 2 8 / 2 2 4 / 2 2 6 / 2 2 8 / 2 2
\/ im (y) + re (y) \/ im (y) + re (y) \/ im (y) + re (y) \/ im (y) + re (y) \/ im (y) + re (y) \/ im (y) + re (y)
$$- \frac{i \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} + \frac{\cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} - \frac{i \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{3} \right)}}{\sqrt[6]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} + \frac{\cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{3} \right)}}{\sqrt[6]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} - \frac{i \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}}{\sqrt[8]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} + \frac{\cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}}{\sqrt[8]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}}$$
cos(atan2(im(y), re(y))/2)/(im(y)^2 + re(y)^2)^(1/4) + cos(atan2(im(y), re(y))/3)/(im(y)^2 + re(y)^2)^(1/6) + cos(atan2(im(y), re(y))/4)/(im(y)^2 + re(y)^2)^(1/8) - i*sin(atan2(im(y), re(y))/2)/(im(y)^2 + re(y)^2)^(1/4) - i*sin(atan2(im(y), re(y))/3)/(im(y)^2 + re(y)^2)^(1/6) - i*sin(atan2(im(y), re(y))/4)/(im(y)^2 + re(y)^2)^(1/8)
Respuesta rápida
[src]
// 3/8 5/12 7/24 \ / 3/8 5/12 7/24 \ \ / 3/8 5/12 7/24 \ / 3/8 5/12 7/24 \
||/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\ |/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\| |/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\ |/ 2 2 \ /3*atan2(im(y), re(y))\ / 2 2 \ /5*atan2(im(y), re(y))\ / 2 2 \ /7*atan2(im(y), re(y))\| /13*atan2(im(y), re(y))\
||\im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------||*cos|----------------------| |\im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------||*sin|----------------------|| |\im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------| + \im (y) + re (y)/ *cos|---------------------||*cos|----------------------| |\im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------| + \im (y) + re (y)/ *sin|---------------------||*sin|----------------------|
|\ \ 4 / \ 6 / \ 12 // \ 12 / \ \ 4 / \ 6 / \ 12 // \ 12 /| \ \ 4 / \ 6 / \ 12 // \ 12 / \ \ 4 / \ 6 / \ 12 // \ 12 /
x1 = I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 13 13 | 13 13
| -- -- | -- --
| 24 24 | 24 24
| / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \
\ \im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/ \im (y) + re (y)/
$$x_{1} = i \left(\frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \sin{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \sin{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \cos{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}} - \frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \cos{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \cos{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \sin{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}}\right) + \frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \sin{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \sin{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \sin{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \sin{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}} + \frac{\left(\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{7}{24}} \cos{\left(\frac{7 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{5}{12}} \cos{\left(\frac{5 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{6} \right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{3}{8}} \cos{\left(\frac{3 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{4} \right)}\right) \cos{\left(\frac{13 \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{12} \right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{\frac{13}{24}}}$$
x1 = i*(((re(y)^2 + im(y)^2)^(7/24)*sin(7*atan2(im(y, re(y))/12) + (re(y)^2 + im(y)^2)^(5/12)*sin(5*atan2(im(y), re(y))/6) + (re(y)^2 + im(y)^2)^(3/8)*sin(3*atan2(im(y), re(y))/4))*cos(13*atan2(im(y), re(y))/12)/(re(y)^2 + im(y)^2)^(13/24) - ((re(y)^2 + im(y)^2)^(7/24)*cos(7*atan2(im(y), re(y))/12) + (re(y)^2 + im(y)^2)^(5/12)*cos(5*atan2(im(y), re(y))/6) + (re(y)^2 + im(y)^2)^(3/8)*cos(3*atan2(im(y), re(y))/4))*sin(13*atan2(im(y), re(y))/12)/(re(y)^2 + im(y)^2)^(13/24)) + ((re(y)^2 + im(y)^2)^(7/24)*sin(7*atan2(im(y), re(y))/12) + (re(y)^2 + im(y)^2)^(5/12)*sin(5*atan2(im(y), re(y))/6) + (re(y)^2 + im(y)^2)^(3/8)*sin(3*atan2(im(y), re(y))/4))*sin(13*atan2(im(y), re(y))/12)/(re(y)^2 + im(y)^2)^(13/24) + ((re(y)^2 + im(y)^2)^(7/24)*cos(7*atan2(im(y), re(y))/12) + (re(y)^2 + im(y)^2)^(5/12)*cos(5*atan2(im(y), re(y))/6) + (re(y)^2 + im(y)^2)^(3/8)*cos(3*atan2(im(y), re(y))/4))*cos(13*atan2(im(y), re(y))/12)/(re(y)^2 + im(y)^2)^(13/24))