Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación 8*x=2
-
Ecuación 3^x=81
-
Ecuación x^2=12
-
Ecuación -27x+220=-5x
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- 9*x+17*y=13
- -17*x+2*y=9
-
Expresiones idénticas
- tres *t^ dos -t*(uno - tres /a)- tres *(dos *a- uno)/a= cero
- 3 multiplicar por t al cuadrado menos t multiplicar por (1 menos 3 dividir por a) menos 3 multiplicar por (2 multiplicar por a menos 1) dividir por a es igual a 0
- tres multiplicar por t en el grado dos menos t multiplicar por (uno menos tres dividir por a) menos tres multiplicar por (dos multiplicar por a menos uno) dividir por a es igual a cero
- 3*t2-t*(1-3/a)-3*(2*a-1)/a=0
- 3*t2-t*1-3/a-3*2*a-1/a=0
- 3*t²-t*(1-3/a)-3*(2*a-1)/a=0
- 3*t en el grado 2-t*(1-3/a)-3*(2*a-1)/a=0
- 3t^2-t(1-3/a)-3(2a-1)/a=0
- 3t2-t(1-3/a)-3(2a-1)/a=0
- 3t2-t1-3/a-32a-1/a=0
- 3t^2-t1-3/a-32a-1/a=0
- 3*t^2-t*(1-3/a)-3*(2*a-1)/a=O
- 3*t^2-t*(1-3 dividir por a)-3*(2*a-1) dividir por a=0
-
Expresiones semejantes
- 3*t^2+t*(1-3/a)-3*(2*a-1)/a=0
- 3*t^2-t*(1+3/a)-3*(2*a-1)/a=0
- 3*t^2-t*(1-3/a)-3*(2*a+1)/a=0
- 3*t^2-t*(1-3/a)+3*(2*a-1)/a=0
3*t^2-t*(1-3/a)-3*(2*a-1)/a=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 / 3\ 3*(2*a - 1)
3*t - t*|1 - -| - ----------- = 0
\ a/ a
$$\left(3 t^{2} - t \left(1 - \frac{3}{a}\right)\right) - \frac{3 \left(2 a - 1\right)}{a} = 0$$
Solución detallada
Abramos la expresión en la ecuación
$$\left(3 t^{2} - t \left(1 - \frac{3}{a}\right)\right) - \frac{3 \left(2 a - 1\right)}{a} = 0$$
Obtenemos la ecuación cuadrática
$$3 t^{2} - t - 6 + \frac{3 t}{a} + \frac{3}{a} = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$t_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$t_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 3$$
$$b = -1 + \frac{3}{a}$$
$$c = -6 + \frac{3}{a}$$
, entonces
La ecuación tiene dos raíces.
o
$$t_{1} = \frac{\sqrt{\left(-1 + \frac{3}{a}\right)^{2} + 72 - \frac{36}{a}}}{6} + \frac{1}{6} - \frac{1}{2 a}$$
$$t_{2} = - \frac{\sqrt{\left(-1 + \frac{3}{a}\right)^{2} + 72 - \frac{36}{a}}}{6} + \frac{1}{6} - \frac{1}{2 a}$$
$$\left(3 t^{2} - t \left(1 - \frac{3}{a}\right)\right) - \frac{3 \left(2 a - 1\right)}{a} = 0$$
Obtenemos la ecuación cuadrática
$$3 t^{2} - t - 6 + \frac{3 t}{a} + \frac{3}{a} = 0$$
Es la ecuación de la forma
a*t^2 + b*t + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$t_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$t_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 3$$
$$b = -1 + \frac{3}{a}$$
$$c = -6 + \frac{3}{a}$$
, entonces
D = b^2 - 4 * a * c =
(-1 + 3/a)^2 - 4 * (3) * (-6 + 3/a) = 72 + (-1 + 3/a)^2 - 36/a
La ecuación tiene dos raíces.
t1 = (-b + sqrt(D)) / (2*a)
t2 = (-b - sqrt(D)) / (2*a)
o
$$t_{1} = \frac{\sqrt{\left(-1 + \frac{3}{a}\right)^{2} + 72 - \frac{36}{a}}}{6} + \frac{1}{6} - \frac{1}{2 a}$$
$$t_{2} = - \frac{\sqrt{\left(-1 + \frac{3}{a}\right)^{2} + 72 - \frac{36}{a}}}{6} + \frac{1}{6} - \frac{1}{2 a}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(3 t^{2} - t \left(1 - \frac{3}{a}\right)\right) - \frac{3 \left(2 a - 1\right)}{a} = 0$$
de
$$a t^{2} + b t + c = 0$$
como ecuación cuadrática reducida
$$t^{2} + \frac{b t}{a} + \frac{c}{a} = 0$$
$$t^{2} - \frac{t \left(1 - \frac{3}{a}\right)}{3} - \frac{6 a - 3}{3 a} = 0$$
$$p t + q + t^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{1}{3} + \frac{1}{a}$$
$$q = \frac{c}{a}$$
$$q = - \frac{2 a - 1}{a}$$
Fórmulas de Cardano-Vieta
$$t_{1} + t_{2} = - p$$
$$t_{1} t_{2} = q$$
$$t_{1} + t_{2} = \frac{1}{3} - \frac{1}{a}$$
$$t_{1} t_{2} = - \frac{2 a - 1}{a}$$
$$\left(3 t^{2} - t \left(1 - \frac{3}{a}\right)\right) - \frac{3 \left(2 a - 1\right)}{a} = 0$$
de
$$a t^{2} + b t + c = 0$$
como ecuación cuadrática reducida
$$t^{2} + \frac{b t}{a} + \frac{c}{a} = 0$$
$$t^{2} - \frac{t \left(1 - \frac{3}{a}\right)}{3} - \frac{6 a - 3}{3 a} = 0$$
$$p t + q + t^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{1}{3} + \frac{1}{a}$$
$$q = \frac{c}{a}$$
$$q = - \frac{2 a - 1}{a}$$
Fórmulas de Cardano-Vieta
$$t_{1} + t_{2} = - p$$
$$t_{1} t_{2} = q$$
$$t_{1} + t_{2} = \frac{1}{3} - \frac{1}{a}$$
$$t_{1} t_{2} = - \frac{2 a - 1}{a}$$
Gráfica
Respuesta rápida
[src]
/ / __________________________________________________________________________ \ / __________________________________________________________________________ \ \ / __________________________________________________________________________ \ / __________________________________________________________________________ \
| | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ |
| | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| |
| |-3 - \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*im(a) |- \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*re(a)| |- \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*im(a) |-3 - \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*re(a)
| \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / /
t1 = I*|- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \
\ 6*\im (a) + re (a)/ 6*\im (a) + re (a)/ / 6*\im (a) + re (a)/ 6*\im (a) + re (a)/
$$t_{1} = \frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}$$
/ / __________________________________________________________________________ \ / __________________________________________________________________________ \ \ / __________________________________________________________________________ \ / __________________________________________________________________________ \
| | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ |
| | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | |4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | |4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| |
| |-3 + \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*im(a) |\/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*re(a)| |\/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*im(a) |-3 + \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*re(a)
| \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / /
t2 = I*|- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \
\ 6*\im (a) + re (a)/ 6*\im (a) + re (a)/ / 6*\im (a) + re (a)/ 6*\im (a) + re (a)/
$$t_{2} = \frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}$$
t2 = (((146*re(a)*im(a) - 42*im(a))^2 + (73*re(a)^2 - 42*re(a) - 73*im(a)^2 + 9)^2)^(1/4)*sin(atan2(146*re(a)*im(a) - 42*im(a, 73*re(a)^2 - 42*re(a) - 73*im(a)^2 + 9)/2) + im(a))*im(a)/(6*(re(a)^2 + im(a)^2)) + i*((((146*re(a)*im(a) - 42*im(a))^2 + (73*re(a)^2 - 42*re(a) - 73*im(a)^2 + 9)^2)^(1/4)*sin(atan2(146*re(a)*im(a) - 42*im(a), 73*re(a)^2 - 42*re(a) - 73*im(a)^2 + 9)/2) + im(a))*re(a)/(6*(re(a)^2 + im(a)^2)) - (((146*re(a)*im(a) - 42*im(a))^2 + (73*re(a)^2 - 42*re(a) - 73*im(a)^2 + 9)^2)^(1/4)*cos(atan2(146*re(a)*im(a) - 42*im(a), 73*re(a)^2 - 42*re(a) - 73*im(a)^2 + 9)/2) + re(a) - 3)*im(a)/(6*(re(a)^2 + im(a)^2))) + (((146*re(a)*im(a) - 42*im(a))^2 + (73*re(a)^2 - 42*re(a) - 73*im(a)^2 + 9)^2)^(1/4)*cos(atan2(146*re(a)*im(a) - 42*im(a), 73*re(a)^2 - 42*re(a) - 73*im(a)^2 + 9)/2) + re(a) - 3)*re(a)/(6*(re(a)^2 + im(a)^2)))
Suma y producto de raíces
[src]
suma
/ / __________________________________________________________________________ \ / __________________________________________________________________________ \ \ / __________________________________________________________________________ \ / __________________________________________________________________________ \ / / __________________________________________________________________________ \ / __________________________________________________________________________ \ \ / __________________________________________________________________________ \ / __________________________________________________________________________ \ | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | |4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | |4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | |-3 - \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*im(a) |- \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*re(a)| |- \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*im(a) |-3 - \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*re(a) | |-3 + \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*im(a) |\/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*re(a)| |\/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*im(a) |-3 + \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*re(a) | \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / / I*|- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + I*|- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ \ 6*\im (a) + re (a)/ 6*\im (a) + re (a)/ / 6*\im (a) + re (a)/ 6*\im (a) + re (a)/ \ 6*\im (a) + re (a)/ 6*\im (a) + re (a)/ / 6*\im (a) + re (a)/ 6*\im (a) + re (a)/
$$\left(\frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \left(\frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right)$$
=
/ / __________________________________________________________________________ \ / __________________________________________________________________________ \ \ / / __________________________________________________________________________ \ / __________________________________________________________________________ \ \ / __________________________________________________________________________ \ / __________________________________________________________________________ \ / __________________________________________________________________________ \ / __________________________________________________________________________ \ | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | |4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | |4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | |-3 + \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*im(a) |\/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*re(a)| | |-3 - \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*im(a) |- \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*re(a)| |\/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*im(a) |- \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*im(a) |-3 + \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*re(a) |-3 - \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*re(a) | \ \ 2 / / \ \ 2 / / | | \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / / \ \ 2 / / \ \ 2 / / I*|- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | / 2 2 \ / 2 2 \ | | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ / 2 2 \ / 2 2 \ \ 6*\im (a) + re (a)/ 6*\im (a) + re (a)/ / \ 6*\im (a) + re (a)/ 6*\im (a) + re (a)/ / 6*\im (a) + re (a)/ 6*\im (a) + re (a)/ 6*\im (a) + re (a)/ 6*\im (a) + re (a)/
$$\frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + i \left(\frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}$$
producto
/ / / __________________________________________________________________________ \ / __________________________________________________________________________ \ \ / __________________________________________________________________________ \ / __________________________________________________________________________ \ \ / / / __________________________________________________________________________ \ / __________________________________________________________________________ \ \ / __________________________________________________________________________ \ / __________________________________________________________________________ \ \ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | | | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | |4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | |4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | 4 / 2 / 2 2 \ |atan2\-42*im(a) + 146*im(a)*re(a), 9 - 73*im (a) - 42*re(a) + 73*re (a)/| | | | | |-3 - \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*im(a) |- \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*re(a)| |- \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*im(a) |-3 - \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*re(a)| | | |-3 + \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*im(a) |\/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*re(a)| |\/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *sin|------------------------------------------------------------------------| + im(a)|*im(a) |-3 + \/ (-42*im(a) + 146*im(a)*re(a)) + \9 - 73*im (a) - 42*re(a) + 73*re (a)/ *cos|------------------------------------------------------------------------| + re(a)|*re(a)| | | \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / / | | | \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / / | |I*|- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|I*|- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ | | | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ | \ \ 6*\im (a) + re (a)/ 6*\im (a) + re (a)/ / 6*\im (a) + re (a)/ 6*\im (a) + re (a)/ / \ \ 6*\im (a) + re (a)/ 6*\im (a) + re (a)/ / 6*\im (a) + re (a)/ 6*\im (a) + re (a)/ /
$$\left(\frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\left(- \sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) \left(\frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{im}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\left(\sqrt[4]{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)}\right)^{2} + \left(73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(146 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 42 \operatorname{im}{\left(a\right)},73 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 42 \operatorname{re}{\left(a\right)} - 73 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} - 3\right) \operatorname{re}{\left(a\right)}}{6 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right)$$
=
/ 2 2 \
-\-re(a) + 2*im (a) + 2*re (a) + I*im(a)/
------------------------------------------
2 2
im (a) + re (a)
$$- \frac{2 \left(\operatorname{re}{\left(a\right)}\right)^{2} - \operatorname{re}{\left(a\right)} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} + i \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
-(-re(a) + 2*im(a)^2 + 2*re(a)^2 + i*im(a))/(im(a)^2 + re(a)^2)