Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación (x-3)*(x+2)=0
-
Ecuación (11x+14)-(5x-8)=25
-
Ecuación z^2-6*z+10=0
-
Ecuación 4/(x-4)=-5
- Expresar {x} en función de y en la ecuación:
- -7*x-13*y=5
- 15*x+1*y=19
- 7*x-1*y=-7
- 20*x+5*y=-3
-
Expresiones idénticas
- dos *(dos *x+ dos *y-z- tres)^ dos = tres *(x^ dos - dos *x+ uno +y^ dos - cuatro *y+ cuatro +z^ dos - seis *z+ nueve)
- 2 multiplicar por (2 multiplicar por x más 2 multiplicar por y menos z menos 3) al cuadrado es igual a 3 multiplicar por (x al cuadrado menos 2 multiplicar por x más 1 más y al cuadrado menos 4 multiplicar por y más 4 más z al cuadrado menos 6 multiplicar por z más 9)
- dos multiplicar por (dos multiplicar por x más dos multiplicar por y menos z menos tres) en el grado dos es igual a tres multiplicar por (x en el grado dos menos dos multiplicar por x más uno más y en el grado dos menos cuatro multiplicar por y más cuatro más z en el grado dos menos seis multiplicar por z más nueve)
- 2*(2*x+2*y-z-3)2=3*(x2-2*x+1+y2-4*y+4+z2-6*z+9)
- 2*2*x+2*y-z-32=3*x2-2*x+1+y2-4*y+4+z2-6*z+9
- 2*(2*x+2*y-z-3)²=3*(x²-2*x+1+y²-4*y+4+z²-6*z+9)
- 2*(2*x+2*y-z-3) en el grado 2=3*(x en el grado 2-2*x+1+y en el grado 2-4*y+4+z en el grado 2-6*z+9)
- 2(2x+2y-z-3)^2=3(x^2-2x+1+y^2-4y+4+z^2-6z+9)
- 2(2x+2y-z-3)2=3(x2-2x+1+y2-4y+4+z2-6z+9)
- 22x+2y-z-32=3x2-2x+1+y2-4y+4+z2-6z+9
- 22x+2y-z-3^2=3x^2-2x+1+y^2-4y+4+z^2-6z+9
-
Expresiones semejantes
- 2*(2*x+2*y-z-3)^2=3*(x^2-2*x-1+y^2-4*y+4+z^2-6*z+9)
- 2*(2*x+2*y+z-3)^2=3*(x^2-2*x+1+y^2-4*y+4+z^2-6*z+9)
- 2*(2*x+2*y-z-3)^2=3*(x^2-2*x+1+y^2-4*y+4+z^2-6*z-9)
- 2*(2*x+2*y-z-3)^2=3*(x^2+2*x+1+y^2-4*y+4+z^2-6*z+9)
- 2*(2*x+2*y-z-3)^2=3*(x^2-2*x+1+y^2-4*y+4+z^2+6*z+9)
- 2*(2*x+2*y-z-3)^2=3*(x^2-2*x+1+y^2-4*y-4+z^2-6*z+9)
- 2*(2*x+2*y-z-3)^2=3*(x^2-2*x+1+y^2+4*y+4+z^2-6*z+9)
- 2*(2*x+2*y-z+3)^2=3*(x^2-2*x+1+y^2-4*y+4+z^2-6*z+9)
- 2*(2*x-2*y-z-3)^2=3*(x^2-2*x+1+y^2-4*y+4+z^2-6*z+9)
- 2*(2*x+2*y-z-3)^2=3*(x^2-2*x+1-y^2-4*y+4+z^2-6*z+9)
- 2*(2*x+2*y-z-3)^2=3*(x^2-2*x+1+y^2-4*y+4-z^2-6*z+9)
2*(2*x+2*y-z-3)^2=3*(x^2-2*x+1+y^2-4*y+4+z^2-6*z+9) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 / 2 2 2 \ 2*(2*x + 2*y - z - 3) = 3*\x - 2*x + 1 + y - 4*y + 4 + z - 6*z + 9/
$$2 \left(\left(- z + \left(2 x + 2 y\right)\right) - 3\right)^{2} = 3 \left(\left(- 6 z + \left(z^{2} + \left(\left(- 4 y + \left(y^{2} + \left(\left(x^{2} - 2 x\right) + 1\right)\right)\right) + 4\right)\right)\right) + 9\right)$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$2 \left(\left(- z + \left(2 x + 2 y\right)\right) - 3\right)^{2} = 3 \left(\left(- 6 z + \left(z^{2} + \left(\left(- 4 y + \left(y^{2} + \left(\left(x^{2} - 2 x\right) + 1\right)\right)\right) + 4\right)\right)\right) + 9\right)$$
en
$$- 3 \left(\left(- 6 z + \left(z^{2} + \left(\left(- 4 y + \left(y^{2} + \left(\left(x^{2} - 2 x\right) + 1\right)\right)\right) + 4\right)\right)\right) + 9\right) + 2 \left(\left(- z + \left(2 x + 2 y\right)\right) - 3\right)^{2} = 0$$
Abramos la expresión en la ecuación
$$- 3 \left(\left(- 6 z + \left(z^{2} + \left(\left(- 4 y + \left(y^{2} + \left(\left(x^{2} - 2 x\right) + 1\right)\right)\right) + 4\right)\right)\right) + 9\right) + 2 \left(\left(- z + \left(2 x + 2 y\right)\right) - 3\right)^{2} = 0$$
Obtenemos la ecuación cuadrática
$$5 x^{2} + 16 x y - 8 x z - 18 x + 5 y^{2} - 8 y z - 12 y - z^{2} + 30 z - 24 = 0$$
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
$$a = 5$$
$$b = 16 y - 8 z - 18$$
$$c = 5 y^{2} - 8 y z - 12 y - z^{2} + 30 z - 24$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = - \frac{8 y}{5} + \frac{4 z}{5} + \frac{\sqrt{- 100 y^{2} + 160 y z + 240 y + 20 z^{2} - 600 z + \left(16 y - 8 z - 18\right)^{2} + 480}}{10} + \frac{9}{5}$$
$$x_{2} = - \frac{8 y}{5} + \frac{4 z}{5} - \frac{\sqrt{- 100 y^{2} + 160 y z + 240 y + 20 z^{2} - 600 z + \left(16 y - 8 z - 18\right)^{2} + 480}}{10} + \frac{9}{5}$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$2 \left(\left(- z + \left(2 x + 2 y\right)\right) - 3\right)^{2} = 3 \left(\left(- 6 z + \left(z^{2} + \left(\left(- 4 y + \left(y^{2} + \left(\left(x^{2} - 2 x\right) + 1\right)\right)\right) + 4\right)\right)\right) + 9\right)$$
en
$$- 3 \left(\left(- 6 z + \left(z^{2} + \left(\left(- 4 y + \left(y^{2} + \left(\left(x^{2} - 2 x\right) + 1\right)\right)\right) + 4\right)\right)\right) + 9\right) + 2 \left(\left(- z + \left(2 x + 2 y\right)\right) - 3\right)^{2} = 0$$
Abramos la expresión en la ecuación
$$- 3 \left(\left(- 6 z + \left(z^{2} + \left(\left(- 4 y + \left(y^{2} + \left(\left(x^{2} - 2 x\right) + 1\right)\right)\right) + 4\right)\right)\right) + 9\right) + 2 \left(\left(- z + \left(2 x + 2 y\right)\right) - 3\right)^{2} = 0$$
Obtenemos la ecuación cuadrática
$$5 x^{2} + 16 x y - 8 x z - 18 x + 5 y^{2} - 8 y z - 12 y - z^{2} + 30 z - 24 = 0$$
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
$$a = 5$$
$$b = 16 y - 8 z - 18$$
$$c = 5 y^{2} - 8 y z - 12 y - z^{2} + 30 z - 24$$
, entonces
D = b^2 - 4 * a * c =
(-18 - 8*z + 16*y)^2 - 4 * (5) * (-24 - z^2 - 12*y + 5*y^2 + 30*z - 8*y*z) = 480 + (-18 - 8*z + 16*y)^2 - 600*z - 100*y^2 + 20*z^2 + 240*y + 160*y*z
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = - \frac{8 y}{5} + \frac{4 z}{5} + \frac{\sqrt{- 100 y^{2} + 160 y z + 240 y + 20 z^{2} - 600 z + \left(16 y - 8 z - 18\right)^{2} + 480}}{10} + \frac{9}{5}$$
$$x_{2} = - \frac{8 y}{5} + \frac{4 z}{5} - \frac{\sqrt{- 100 y^{2} + 160 y z + 240 y + 20 z^{2} - 600 z + \left(16 y - 8 z - 18\right)^{2} + 480}}{10} + \frac{9}{5}$$
Gráfica
Respuesta rápida
[src]
/ ____________________________________________________________________________________________________________________________________________________________________ \ ____________________________________________________________________________________________________________________________________________________________________
| / 2 / / 2 2 2 2 \\| / 2 / / 2 2 2 2 \\
| 4 / 2 / 2 2 2 2 \ |atan2\-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y), 201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/|| 4 / 2 / 2 2 2 2 \ |atan2\-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y), 201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/|
| \/ (-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y)) + \201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------|| \/ (-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y)) + \201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/ *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------|
9 8*re(y) 4*re(z) | 8*im(y) 4*im(z) \ 2 /| \ 2 /
x1 = - - ------- + ------- + I*|- ------- + ------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
5 5 5 \ 5 5 5 / 5
$$x_{1} = - \frac{\sqrt[4]{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)},39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201 \right)}}{2} \right)}}{5} + i \left(- \frac{\sqrt[4]{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)},39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201 \right)}}{2} \right)}}{5} - \frac{8 \operatorname{im}{\left(y\right)}}{5} + \frac{4 \operatorname{im}{\left(z\right)}}{5}\right) - \frac{8 \operatorname{re}{\left(y\right)}}{5} + \frac{4 \operatorname{re}{\left(z\right)}}{5} + \frac{9}{5}$$
/ ____________________________________________________________________________________________________________________________________________________________________ \ ____________________________________________________________________________________________________________________________________________________________________
| / 2 / / 2 2 2 2 \\| / 2 / / 2 2 2 2 \\
| 4 / 2 / 2 2 2 2 \ |atan2\-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y), 201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/|| 4 / 2 / 2 2 2 2 \ |atan2\-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y), 201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/|
| \/ (-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y)) + \201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------|| \/ (-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y)) + \201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/ *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------|
9 8*re(y) 4*re(z) | 8*im(y) 4*im(z) \ 2 /| \ 2 /
x2 = - - ------- + ------- + I*|- ------- + ------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
5 5 5 \ 5 5 5 / 5
$$x_{2} = \frac{\sqrt[4]{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)},39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201 \right)}}{2} \right)}}{5} + i \left(\frac{\sqrt[4]{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)},39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201 \right)}}{2} \right)}}{5} - \frac{8 \operatorname{im}{\left(y\right)}}{5} + \frac{4 \operatorname{im}{\left(z\right)}}{5}\right) - \frac{8 \operatorname{re}{\left(y\right)}}{5} + \frac{4 \operatorname{re}{\left(z\right)}}{5} + \frac{9}{5}$$
x2 = ((78*re(y)*im(y) + 42*re(z)*im(z) - 84*im(y) - 78*im(z) - 24*im(y*z))^2 + (39*re(y)^2 - 84*re(y) + 21*re(z)^2 - 78*re(z) - 24*re(y*z) - 39*im(y)^2 - 21*im(z)^2 + 201)^2)^(1/4)*cos(atan2(78*re(y)*im(y) + 42*re(z)*im(z) - 84*im(y) - 78*im(z) - 24*im(y*z, 39*re(y)^2 - 84*re(y) + 21*re(z)^2 - 78*re(z) - 24*re(y*z) - 39*im(y)^2 - 21*im(z)^2 + 201)/2)/5 + i*(((78*re(y)*im(y) + 42*re(z)*im(z) - 84*im(y) - 78*im(z) - 24*im(y*z))^2 + (39*re(y)^2 - 84*re(y) + 21*re(z)^2 - 78*re(z) - 24*re(y*z) - 39*im(y)^2 - 21*im(z)^2 + 201)^2)^(1/4)*sin(atan2(78*re(y)*im(y) + 42*re(z)*im(z) - 84*im(y) - 78*im(z) - 24*im(y*z), 39*re(y)^2 - 84*re(y) + 21*re(z)^2 - 78*re(z) - 24*re(y*z) - 39*im(y)^2 - 21*im(z)^2 + 201)/2)/5 - 8*im(y)/5 + 4*im(z)/5) - 8*re(y)/5 + 4*re(z)/5 + 9/5)
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 \\
| 4 / 2 / 2 2 2 2 \ |atan2\-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y), 201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/|| 4 / 2 / 2 2 2 2 \ |atan2\-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y), 201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/| | 4 / 2 / 2 2 2 2 \ |atan2\-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y), 201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/|| 4 / 2 / 2 2 2 2 \ |atan2\-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y), 201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/|
| \/ (-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y)) + \201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------|| \/ (-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y)) + \201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/ *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------| | \/ (-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y)) + \201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------|| \/ (-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y)) + \201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/ *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------|
9 8*re(y) 4*re(z) | 8*im(y) 4*im(z) \ 2 /| \ 2 / 9 8*re(y) 4*re(z) | 8*im(y) 4*im(z) \ 2 /| \ 2 /
- - ------- + ------- + I*|- ------- + ------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + - - ------- + ------- + I*|- ------- + ------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
5 5 5 \ 5 5 5 / 5 5 5 5 \ 5 5 5 / 5
$$\left(- \frac{\sqrt[4]{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)},39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201 \right)}}{2} \right)}}{5} + i \left(- \frac{\sqrt[4]{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)},39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201 \right)}}{2} \right)}}{5} - \frac{8 \operatorname{im}{\left(y\right)}}{5} + \frac{4 \operatorname{im}{\left(z\right)}}{5}\right) - \frac{8 \operatorname{re}{\left(y\right)}}{5} + \frac{4 \operatorname{re}{\left(z\right)}}{5} + \frac{9}{5}\right) + \left(\frac{\sqrt[4]{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)},39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201 \right)}}{2} \right)}}{5} + i \left(\frac{\sqrt[4]{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)},39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201 \right)}}{2} \right)}}{5} - \frac{8 \operatorname{im}{\left(y\right)}}{5} + \frac{4 \operatorname{im}{\left(z\right)}}{5}\right) - \frac{8 \operatorname{re}{\left(y\right)}}{5} + \frac{4 \operatorname{re}{\left(z\right)}}{5} + \frac{9}{5}\right)$$
=
/ ____________________________________________________________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________________________________________________________ \
| / 2 / / 2 2 2 2 \\| | / 2 / / 2 2 2 2 \\|
| 4 / 2 / 2 2 2 2 \ |atan2\-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y), 201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/|| | 4 / 2 / 2 2 2 2 \ |atan2\-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y), 201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/||
| \/ (-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y)) + \201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------|| | \/ (-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y)) + \201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------||
18 16*re(y) 8*re(z) | 8*im(y) 4*im(z) \ 2 /| | 8*im(y) 4*im(z) \ 2 /|
-- - -------- + ------- + I*|- ------- + ------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|- ------- + ------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
5 5 5 \ 5 5 5 / \ 5 5 5 /
$$i \left(- \frac{\sqrt[4]{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)},39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201 \right)}}{2} \right)}}{5} - \frac{8 \operatorname{im}{\left(y\right)}}{5} + \frac{4 \operatorname{im}{\left(z\right)}}{5}\right) + i \left(\frac{\sqrt[4]{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)},39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201 \right)}}{2} \right)}}{5} - \frac{8 \operatorname{im}{\left(y\right)}}{5} + \frac{4 \operatorname{im}{\left(z\right)}}{5}\right) - \frac{16 \operatorname{re}{\left(y\right)}}{5} + \frac{8 \operatorname{re}{\left(z\right)}}{5} + \frac{18}{5}$$
producto
/ / ____________________________________________________________________________________________________________________________________________________________________ \ ____________________________________________________________________________________________________________________________________________________________________ \ / / ____________________________________________________________________________________________________________________________________________________________________ \ ____________________________________________________________________________________________________________________________________________________________________ \ | | / 2 / / 2 2 2 2 \\| / 2 / / 2 2 2 2 \\| | | / 2 / / 2 2 2 2 \\| / 2 / / 2 2 2 2 \\| | | 4 / 2 / 2 2 2 2 \ |atan2\-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y), 201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/|| 4 / 2 / 2 2 2 2 \ |atan2\-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y), 201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/|| | | 4 / 2 / 2 2 2 2 \ |atan2\-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y), 201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/|| 4 / 2 / 2 2 2 2 \ |atan2\-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y), 201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/|| | | \/ (-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y)) + \201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------|| \/ (-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y)) + \201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/ *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------|| | | \/ (-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y)) + \201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/ *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------|| \/ (-84*im(y) - 78*im(z) - 24*im(y*z) + 42*im(z)*re(z) + 78*im(y)*re(y)) + \201 - 84*re(y) - 78*re(z) - 39*im (y) - 24*re(y*z) - 21*im (z) + 21*re (z) + 39*re (y)/ *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------|| |9 8*re(y) 4*re(z) | 8*im(y) 4*im(z) \ 2 /| \ 2 /| |9 8*re(y) 4*re(z) | 8*im(y) 4*im(z) \ 2 /| \ 2 /| |- - ------- + ------- + I*|- ------- + ------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|- - ------- + ------- + I*|- ------- + ------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \5 5 5 \ 5 5 5 / 5 / \5 5 5 \ 5 5 5 / 5 /
$$\left(- \frac{\sqrt[4]{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)},39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201 \right)}}{2} \right)}}{5} + i \left(- \frac{\sqrt[4]{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)},39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201 \right)}}{2} \right)}}{5} - \frac{8 \operatorname{im}{\left(y\right)}}{5} + \frac{4 \operatorname{im}{\left(z\right)}}{5}\right) - \frac{8 \operatorname{re}{\left(y\right)}}{5} + \frac{4 \operatorname{re}{\left(z\right)}}{5} + \frac{9}{5}\right) \left(\frac{\sqrt[4]{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)},39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201 \right)}}{2} \right)}}{5} + i \left(\frac{\sqrt[4]{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)}\right)^{2} + \left(39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(78 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 42 \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)} - 84 \operatorname{im}{\left(y\right)} - 78 \operatorname{im}{\left(z\right)} - 24 \operatorname{im}{\left(y z\right)},39 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 84 \operatorname{re}{\left(y\right)} + 21 \left(\operatorname{re}{\left(z\right)}\right)^{2} - 78 \operatorname{re}{\left(z\right)} - 24 \operatorname{re}{\left(y z\right)} - 39 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 21 \left(\operatorname{im}{\left(z\right)}\right)^{2} + 201 \right)}}{2} \right)}}{5} - \frac{8 \operatorname{im}{\left(y\right)}}{5} + \frac{4 \operatorname{im}{\left(z\right)}}{5}\right) - \frac{8 \operatorname{re}{\left(y\right)}}{5} + \frac{4 \operatorname{re}{\left(z\right)}}{5} + \frac{9}{5}\right)$$
=
2 2 24 2 2 12*re(y) re (z) im (z) 24*re(y*z) 64*re(y)*re(z) 12*I*im(y) 24*I*im(y*z) 64*im(y)*im(z) 64*I*im(y)*re(z) 64*I*im(z)*re(y) 2*I*im(z)*re(z) - -- + re (y) - im (y) + 6*re(z) - -------- - ------ + ------ + ---------- + 6*I*im(z) - -------------- - ---------- + ------------ + -------------- + 2*I*im(y)*re(y) - ---------------- - ---------------- - --------------- 5 5 5 5 25 25 5 25 25 25 25 5
$$\left(\operatorname{re}{\left(y\right)}\right)^{2} - \frac{64 \operatorname{re}{\left(y\right)} \operatorname{re}{\left(z\right)}}{25} + 2 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \frac{64 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(z\right)}}{25} - \frac{12 \operatorname{re}{\left(y\right)}}{5} - \frac{\left(\operatorname{re}{\left(z\right)}\right)^{2}}{5} - \frac{64 i \operatorname{re}{\left(z\right)} \operatorname{im}{\left(y\right)}}{25} - \frac{2 i \operatorname{re}{\left(z\right)} \operatorname{im}{\left(z\right)}}{5} + 6 \operatorname{re}{\left(z\right)} + \frac{24 \operatorname{re}{\left(y z\right)}}{25} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + \frac{64 \operatorname{im}{\left(y\right)} \operatorname{im}{\left(z\right)}}{25} - \frac{12 i \operatorname{im}{\left(y\right)}}{5} + \frac{\left(\operatorname{im}{\left(z\right)}\right)^{2}}{5} + 6 i \operatorname{im}{\left(z\right)} + \frac{24 i \operatorname{im}{\left(y z\right)}}{25} - \frac{24}{5}$$
-24/5 + re(y)^2 - im(y)^2 + 6*re(z) - 12*re(y)/5 - re(z)^2/5 + im(z)^2/5 + 24*re(y*z)/25 + 6*i*im(z) - 64*re(y)*re(z)/25 - 12*i*im(y)/5 + 24*i*im(y*z)/25 + 64*im(y)*im(z)/25 + 2*i*im(y)*re(y) - 64*i*im(y)*re(z)/25 - 64*i*im(z)*re(y)/25 - 2*i*im(z)*re(z)/5