Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
-
Ecuación x(x^2+2x+1)=6(x+1)
-
Ecuación 4x+1=-3x+15
- Ecuación (3x−36)⋅(x+8)=0
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 13*x-12*y=19
- -9*x+11*y=9
- -4*x-8*y=-20
-
Expresiones idénticas
- atan(y/ tres)/ tres =Const+x^ dos / dos
- arco tangente de gente de (y dividir por 3) dividir por 3 es igual a Const más x al cuadrado dividir por 2
- arco tangente de gente de (y dividir por tres) dividir por tres es igual a Const más x en el grado dos dividir por dos
- atan(y/3)/3=Const+x2/2
- atany/3/3=Const+x2/2
- atan(y/3)/3=Const+x²/2
- atan(y/3)/3=Const+x en el grado 2/2
- atany/3/3=Const+x^2/2
- atan(y dividir por 3) dividir por 3=Const+x^2 dividir por 2
-
Expresiones semejantes
- atan(y/3)/3=Const-x^2/2
- arctan(y/3)/3=Const+x^2/2
-
Expresiones con funciones
- Arcotangente arctan
- atan(1/x)=o*(1)
- atan(x)-x^2+1=0
- atan(x)-(1/x^3)=0
- atan(x)+atan(3*x)=atan(4*x/(1-3*x^2))
- atan((x-1)/2)=1,6388
atan(y/3)/3=Const+x^2/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/y\
atan|-| 2
\3/ x
------- = c + --
3 2
$$\frac{\operatorname{atan}{\left(\frac{y}{3} \right)}}{3} = c + \frac{x^{2}}{2}$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$\frac{\operatorname{atan}{\left(\frac{y}{3} \right)}}{3} = c + \frac{x^{2}}{2}$$
en
$$\left(- c - \frac{x^{2}}{2}\right) + \frac{\operatorname{atan}{\left(\frac{y}{3} \right)}}{3} = 0$$
Abramos la expresión en la ecuación
$$\left(- c - \frac{x^{2}}{2}\right) + \frac{\operatorname{atan}{\left(\frac{y}{3} \right)}}{3} = 0$$
Obtenemos la ecuación cuadrática
$$- c - \frac{x^{2}}{2} + \frac{\operatorname{atan}{\left(\frac{y}{3} \right)}}{3} = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = - \frac{1}{2}$$
$$b = 0$$
$$c = - c + \frac{\operatorname{atan}{\left(\frac{y}{3} \right)}}{3}$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = - \sqrt{- 2 c + \frac{2 \operatorname{atan}{\left(\frac{y}{3} \right)}}{3}}$$
$$x_{2} = \sqrt{- 2 c + \frac{2 \operatorname{atan}{\left(\frac{y}{3} \right)}}{3}}$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$\frac{\operatorname{atan}{\left(\frac{y}{3} \right)}}{3} = c + \frac{x^{2}}{2}$$
en
$$\left(- c - \frac{x^{2}}{2}\right) + \frac{\operatorname{atan}{\left(\frac{y}{3} \right)}}{3} = 0$$
Abramos la expresión en la ecuación
$$\left(- c - \frac{x^{2}}{2}\right) + \frac{\operatorname{atan}{\left(\frac{y}{3} \right)}}{3} = 0$$
Obtenemos la ecuación cuadrática
$$- c - \frac{x^{2}}{2} + \frac{\operatorname{atan}{\left(\frac{y}{3} \right)}}{3} = 0$$
Es la ecuación de la forma
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = - \frac{1}{2}$$
$$b = 0$$
$$c = - c + \frac{\operatorname{atan}{\left(\frac{y}{3} \right)}}{3}$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-1/2) * (-c + atan(y/3)/3) = -2*c + 2*atan(y/3)/3
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = - \sqrt{- 2 c + \frac{2 \operatorname{atan}{\left(\frac{y}{3} \right)}}{3}}$$
$$x_{2} = \sqrt{- 2 c + \frac{2 \operatorname{atan}{\left(\frac{y}{3} \right)}}{3}}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\frac{\operatorname{atan}{\left(\frac{y}{3} \right)}}{3} = c + \frac{x^{2}}{2}$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$2 c + x^{2} - \frac{2 \operatorname{atan}{\left(\frac{y}{3} \right)}}{3} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 2 c - \frac{2 \operatorname{atan}{\left(\frac{y}{3} \right)}}{3}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 2 c - \frac{2 \operatorname{atan}{\left(\frac{y}{3} \right)}}{3}$$
$$\frac{\operatorname{atan}{\left(\frac{y}{3} \right)}}{3} = c + \frac{x^{2}}{2}$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$2 c + x^{2} - \frac{2 \operatorname{atan}{\left(\frac{y}{3} \right)}}{3} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 2 c - \frac{2 \operatorname{atan}{\left(\frac{y}{3} \right)}}{3}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 2 c - \frac{2 \operatorname{atan}{\left(\frac{y}{3} \right)}}{3}$$
Gráfica
Respuesta rápida
[src]
_____________________________________________________________ / / / /y\\ / /y\\\\ _____________________________________________________________ / / / /y\\ / /y\\\\
/ 2 2 |atan2|-18*im(c) + 6*im|atan|-||, -18*re(c) + 6*re|atan|-|||| / 2 2 |atan2|-18*im(c) + 6*im|atan|-||, -18*re(c) + 6*re|atan|-||||
/ / / /y\\\ / / /y\\\ | \ \ \3// \ \3///| / / / /y\\\ / / /y\\\ | \ \ \3// \ \3///|
4 / |-18*im(c) + 6*im|atan|-||| + |-18*re(c) + 6*re|atan|-||| *cos|-----------------------------------------------------------| I*4 / |-18*im(c) + 6*im|atan|-||| + |-18*re(c) + 6*re|atan|-||| *sin|-----------------------------------------------------------|
\/ \ \ \3/// \ \ \3/// \ 2 / \/ \ \ \3/// \ \ \3/// \ 2 /
x1 = - ----------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------
3 3
$$x_{1} = - \frac{i \sqrt[4]{\left(- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2} + \left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)},- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)} \right)}}{2} \right)}}{3} - \frac{\sqrt[4]{\left(- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2} + \left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)},- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)} \right)}}{2} \right)}}{3}$$
_____________________________________________________________ / / / /y\\ / /y\\\\ _____________________________________________________________ / / / /y\\ / /y\\\\
/ 2 2 |atan2|-18*im(c) + 6*im|atan|-||, -18*re(c) + 6*re|atan|-|||| / 2 2 |atan2|-18*im(c) + 6*im|atan|-||, -18*re(c) + 6*re|atan|-||||
/ / / /y\\\ / / /y\\\ | \ \ \3// \ \3///| / / / /y\\\ / / /y\\\ | \ \ \3// \ \3///|
4 / |-18*im(c) + 6*im|atan|-||| + |-18*re(c) + 6*re|atan|-||| *cos|-----------------------------------------------------------| I*4 / |-18*im(c) + 6*im|atan|-||| + |-18*re(c) + 6*re|atan|-||| *sin|-----------------------------------------------------------|
\/ \ \ \3/// \ \ \3/// \ 2 / \/ \ \ \3/// \ \ \3/// \ 2 /
x2 = ----------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------
3 3
$$x_{2} = \frac{i \sqrt[4]{\left(- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2} + \left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)},- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)} \right)}}{2} \right)}}{3} + \frac{\sqrt[4]{\left(- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2} + \left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)},- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)} \right)}}{2} \right)}}{3}$$
x2 = i*((-18*re(c) + 6*re(atan(y/3)))^2 + (-18*im(c) + 6*im(atan(y/3)))^2)^(1/4)*sin(atan2(-18*im(c) + 6*im(atan(y/3), -18*re(c) + 6*re(atan(y/3)))/2)/3 + ((-18*re(c) + 6*re(atan(y/3)))^2 + (-18*im(c) + 6*im(atan(y/3)))^2)^(1/4)*cos(atan2(-18*im(c) + 6*im(atan(y/3)), -18*re(c) + 6*re(atan(y/3)))/2)/3)
Suma y producto de raíces
[src]
suma
_____________________________________________________________ / / / /y\\ / /y\\\\ _____________________________________________________________ / / / /y\\ / /y\\\\ _____________________________________________________________ / / / /y\\ / /y\\\\ _____________________________________________________________ / / / /y\\ / /y\\\\
/ 2 2 |atan2|-18*im(c) + 6*im|atan|-||, -18*re(c) + 6*re|atan|-|||| / 2 2 |atan2|-18*im(c) + 6*im|atan|-||, -18*re(c) + 6*re|atan|-|||| / 2 2 |atan2|-18*im(c) + 6*im|atan|-||, -18*re(c) + 6*re|atan|-|||| / 2 2 |atan2|-18*im(c) + 6*im|atan|-||, -18*re(c) + 6*re|atan|-||||
/ / / /y\\\ / / /y\\\ | \ \ \3// \ \3///| / / / /y\\\ / / /y\\\ | \ \ \3// \ \3///| / / / /y\\\ / / /y\\\ | \ \ \3// \ \3///| / / / /y\\\ / / /y\\\ | \ \ \3// \ \3///|
4 / |-18*im(c) + 6*im|atan|-||| + |-18*re(c) + 6*re|atan|-||| *cos|-----------------------------------------------------------| I*4 / |-18*im(c) + 6*im|atan|-||| + |-18*re(c) + 6*re|atan|-||| *sin|-----------------------------------------------------------| 4 / |-18*im(c) + 6*im|atan|-||| + |-18*re(c) + 6*re|atan|-||| *cos|-----------------------------------------------------------| I*4 / |-18*im(c) + 6*im|atan|-||| + |-18*re(c) + 6*re|atan|-||| *sin|-----------------------------------------------------------|
\/ \ \ \3/// \ \ \3/// \ 2 / \/ \ \ \3/// \ \ \3/// \ 2 / \/ \ \ \3/// \ \ \3/// \ 2 / \/ \ \ \3/// \ \ \3/// \ 2 /
- ----------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------
3 3 3 3
$$\left(- \frac{i \sqrt[4]{\left(- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2} + \left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)},- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)} \right)}}{2} \right)}}{3} - \frac{\sqrt[4]{\left(- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2} + \left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)},- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)} \right)}}{2} \right)}}{3}\right) + \left(\frac{i \sqrt[4]{\left(- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2} + \left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)},- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)} \right)}}{2} \right)}}{3} + \frac{\sqrt[4]{\left(- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2} + \left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)},- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)} \right)}}{2} \right)}}{3}\right)$$
=
0
$$0$$
producto
/ _____________________________________________________________ / / / /y\\ / /y\\\\ _____________________________________________________________ / / / /y\\ / /y\\\\\ / _____________________________________________________________ / / / /y\\ / /y\\\\ _____________________________________________________________ / / / /y\\ / /y\\\\\ | / 2 2 |atan2|-18*im(c) + 6*im|atan|-||, -18*re(c) + 6*re|atan|-|||| / 2 2 |atan2|-18*im(c) + 6*im|atan|-||, -18*re(c) + 6*re|atan|-||||| | / 2 2 |atan2|-18*im(c) + 6*im|atan|-||, -18*re(c) + 6*re|atan|-|||| / 2 2 |atan2|-18*im(c) + 6*im|atan|-||, -18*re(c) + 6*re|atan|-||||| | / / / /y\\\ / / /y\\\ | \ \ \3// \ \3///| / / / /y\\\ / / /y\\\ | \ \ \3// \ \3///|| | / / / /y\\\ / / /y\\\ | \ \ \3// \ \3///| / / / /y\\\ / / /y\\\ | \ \ \3// \ \3///|| | 4 / |-18*im(c) + 6*im|atan|-||| + |-18*re(c) + 6*re|atan|-||| *cos|-----------------------------------------------------------| I*4 / |-18*im(c) + 6*im|atan|-||| + |-18*re(c) + 6*re|atan|-||| *sin|-----------------------------------------------------------|| |4 / |-18*im(c) + 6*im|atan|-||| + |-18*re(c) + 6*re|atan|-||| *cos|-----------------------------------------------------------| I*4 / |-18*im(c) + 6*im|atan|-||| + |-18*re(c) + 6*re|atan|-||| *sin|-----------------------------------------------------------|| | \/ \ \ \3/// \ \ \3/// \ 2 / \/ \ \ \3/// \ \ \3/// \ 2 /| |\/ \ \ \3/// \ \ \3/// \ 2 / \/ \ \ \3/// \ \ \3/// \ 2 /| |- ----------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------|*|----------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------| \ 3 3 / \ 3 3 /
$$\left(- \frac{i \sqrt[4]{\left(- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2} + \left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)},- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)} \right)}}{2} \right)}}{3} - \frac{\sqrt[4]{\left(- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2} + \left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)},- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)} \right)}}{2} \right)}}{3}\right) \left(\frac{i \sqrt[4]{\left(- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2} + \left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)},- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)} \right)}}{2} \right)}}{3} + \frac{\sqrt[4]{\left(- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2} + \left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)},- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)} \right)}}{2} \right)}}{3}\right)$$
=
_________________________________________________________ / / /y\\ / /y\\\
/ 2 2 I*atan2|-18*im(c) + 6*im|atan|-||, -18*re(c) + 6*re|atan|-|||
/ / / /y\\ \ / / /y\\ \ \ \ \3// \ \3///
-2* / |- im|atan|-|| + 3*im(c)| + |- re|atan|-|| + 3*re(c)| *e
\/ \ \ \3// / \ \ \3// /
--------------------------------------------------------------------------------------------------------------------------------
3
$$- \frac{2 \sqrt{\left(3 \operatorname{re}{\left(c\right)} - \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2} + \left(3 \operatorname{im}{\left(c\right)} - \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(- 18 \operatorname{im}{\left(c\right)} + 6 \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)},- 18 \operatorname{re}{\left(c\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y}{3} \right)}\right)} \right)}}}{3}$$
-2*sqrt((-im(atan(y/3)) + 3*im(c))^2 + (-re(atan(y/3)) + 3*re(c))^2)*exp(i*atan2(-18*im(c) + 6*im(atan(y/3)), -18*re(c) + 6*re(atan(y/3))))/3