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Expresiones semejantes
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x+1/x+3-12/x2-9=2-x/3-x la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
1 12 x
x + - + 3 - -- - 9 = 2 - - - x
x x2 3
$$\left(\left(\left(x + \frac{1}{x}\right) + 3\right) - \frac{12}{x_{2}}\right) - 9 = - x + \left(- \frac{x}{3} + 2\right)$$
Solución detallada
Tenemos la ecuación:
$$\left(\left(\left(x + \frac{1}{x}\right) + 3\right) - \frac{12}{x_{2}}\right) - 9 = - x + \left(- \frac{x}{3} + 2\right)$$
Multipliquemos las dos partes de la ecuación por los denominadores:
y x
obtendremos:
$$x \left(\left(\left(\left(x + \frac{1}{x}\right) + 3\right) - \frac{12}{x_{2}}\right) - 9\right) = x \left(- x + \left(- \frac{x}{3} + 2\right)\right)$$
$$x^{2} - 6 x - \frac{12 x}{x_{2}} + 1 = - \frac{4 x^{2}}{3} + 2 x$$
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$x^{2} - 6 x - \frac{12 x}{x_{2}} + 1 = - \frac{4 x^{2}}{3} + 2 x$$
en
$$\frac{7 x^{2}}{3} - 8 x - \frac{12 x}{x_{2}} + 1 = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = \frac{7}{3}$$
$$b = -8 - \frac{12}{x_{2}}$$
$$c = 1$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{3 \sqrt{\left(-8 - \frac{12}{x_{2}}\right)^{2} - \frac{28}{3}}}{14} + \frac{12}{7} + \frac{18}{7 x_{2}}$$
$$x_{2} = - \frac{3 \sqrt{\left(-8 - \frac{12}{x_{2}}\right)^{2} - \frac{28}{3}}}{14} + \frac{12}{7} + \frac{18}{7 x_{2}}$$
$$\left(\left(\left(x + \frac{1}{x}\right) + 3\right) - \frac{12}{x_{2}}\right) - 9 = - x + \left(- \frac{x}{3} + 2\right)$$
Multipliquemos las dos partes de la ecuación por los denominadores:
y x
obtendremos:
$$x \left(\left(\left(\left(x + \frac{1}{x}\right) + 3\right) - \frac{12}{x_{2}}\right) - 9\right) = x \left(- x + \left(- \frac{x}{3} + 2\right)\right)$$
$$x^{2} - 6 x - \frac{12 x}{x_{2}} + 1 = - \frac{4 x^{2}}{3} + 2 x$$
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$x^{2} - 6 x - \frac{12 x}{x_{2}} + 1 = - \frac{4 x^{2}}{3} + 2 x$$
en
$$\frac{7 x^{2}}{3} - 8 x - \frac{12 x}{x_{2}} + 1 = 0$$
Es la ecuación de la forma
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = \frac{7}{3}$$
$$b = -8 - \frac{12}{x_{2}}$$
$$c = 1$$
, entonces
D = b^2 - 4 * a * c =
(-8 - 12/x2)^2 - 4 * (7/3) * (1) = -28/3 + (-8 - 12/x2)^2
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{3 \sqrt{\left(-8 - \frac{12}{x_{2}}\right)^{2} - \frac{28}{3}}}{14} + \frac{12}{7} + \frac{18}{7 x_{2}}$$
$$x_{2} = - \frac{3 \sqrt{\left(-8 - \frac{12}{x_{2}}\right)^{2} - \frac{28}{3}}}{14} + \frac{12}{7} + \frac{18}{7 x_{2}}$$
Gráfica
Respuesta rápida
[src]
// _____________________________________________________________________________________ \ / _____________________________________________________________________________________ \ \ / _____________________________________________________________________________________ \ / _____________________________________________________________________________________ \
|| / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
|| 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/||
|| \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------|| | | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------||
||12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /| | |12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /|
||--------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2) |-- + --------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2)| |--------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2) |-- + --------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2)
|\ 7 7 / \7 7 7 / | \ 7 7 / \7 7 7 /
x1 = I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 2 2 2 | 2 2 2 2
\ im (x2) + re (x2) im (x2) + re (x2) / im (x2) + re (x2) im (x2) + re (x2)
$$x_{1} = \frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} + i \left(\frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} - \frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}\right) + \frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}$$
// _____________________________________________________________________________________ \ / _____________________________________________________________________________________ \ \ / _____________________________________________________________________________________ \ / _____________________________________________________________________________________ \
|| / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
|| 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/||
|| \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------|| | | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------||
||12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /| | |12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /|
||--------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2) |-- + --------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2)| |--------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2) |-- + --------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2)
|\ 7 7 / \7 7 7 / | \ 7 7 / \7 7 7 /
x2 = I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 2 2 2 | 2 2 2 2
\ im (x2) + re (x2) im (x2) + re (x2) / im (x2) + re (x2) im (x2) + re (x2)
$$x_{2} = \frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} + i \left(\frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} - \frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}\right) + \frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}$$
x2 = (((246*re(x2)*im(x2) + 432*im(x2))^2 + (123*re(x2)^2 + 432*re(x2) - 123*im(x2)^2 + 324)^2)^(1/4)*sin(atan2(246*re(x2)*im(x2) + 432*im(x2, 123*re(x2)^2 + 432*re(x2) - 123*im(x2)^2 + 324)/2)/7 + 12*im(x2)/7)*im(x2)/(re(x2)^2 + im(x2)^2) + i*((((246*re(x2)*im(x2) + 432*im(x2))^2 + (123*re(x2)^2 + 432*re(x2) - 123*im(x2)^2 + 324)^2)^(1/4)*sin(atan2(246*re(x2)*im(x2) + 432*im(x2), 123*re(x2)^2 + 432*re(x2) - 123*im(x2)^2 + 324)/2)/7 + 12*im(x2)/7)*re(x2)/(re(x2)^2 + im(x2)^2) - (((246*re(x2)*im(x2) + 432*im(x2))^2 + (123*re(x2)^2 + 432*re(x2) - 123*im(x2)^2 + 324)^2)^(1/4)*cos(atan2(246*re(x2)*im(x2) + 432*im(x2), 123*re(x2)^2 + 432*re(x2) - 123*im(x2)^2 + 324)/2)/7 + 12*re(x2)/7 + 18/7)*im(x2)/(re(x2)^2 + im(x2)^2)) + (((246*re(x2)*im(x2) + 432*im(x2))^2 + (123*re(x2)^2 + 432*re(x2) - 123*im(x2)^2 + 324)^2)^(1/4)*cos(atan2(246*re(x2)*im(x2) + 432*im(x2), 123*re(x2)^2 + 432*re(x2) - 123*im(x2)^2 + 324)/2)/7 + 12*re(x2)/7 + 18/7)*re(x2)/(re(x2)^2 + im(x2)^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\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| || 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| || \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------|| | | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------|| || \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------|| | | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------|| ||12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /| | |12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /| ||12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /| | |12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /| ||--------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2) |-- + --------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2)| |--------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2) |-- + --------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2) ||--------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2) |-- + --------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2)| |--------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2) |-- + --------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2) |\ 7 7 / \7 7 7 / | \ 7 7 / \7 7 7 / |\ 7 7 / \7 7 7 / | \ 7 7 / \7 7 7 / I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | 2 2 2 2 | 2 2 2 2 | 2 2 2 2 | 2 2 2 2 \ im (x2) + re (x2) im (x2) + re (x2) / im (x2) + re (x2) im (x2) + re (x2) \ im (x2) + re (x2) im (x2) + re (x2) / im (x2) + re (x2) im (x2) + re (x2)
$$\left(\frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} + i \left(\frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} - \frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}\right) + \frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}\right) + \left(\frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} + i \left(\frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} - \frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}\right) + \frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}\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\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | || 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| || \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------|| | || \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------|| | | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------|| ||12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /| | ||12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /| | |12*im(x2) \ 2 /| |12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /| |18 12*re(x2) \ 2 /| ||--------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2) |-- + --------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2)| ||--------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2) |-- + --------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2)| |--------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2) |--------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2) |-- + --------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2) |-- + --------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2) |\ 7 7 / \7 7 7 / | |\ 7 7 / \7 7 7 / | \ 7 7 / \ 7 7 / \7 7 7 / \7 7 7 / I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | 2 2 2 2 | | 2 2 2 2 | 2 2 2 2 2 2 2 2 \ im (x2) + re (x2) im (x2) + re (x2) / \ im (x2) + re (x2) im (x2) + re (x2) / im (x2) + re (x2) im (x2) + re (x2) im (x2) + re (x2) im (x2) + re (x2)
$$\frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} + \frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} + i \left(\frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} - \frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}\right) + i \left(\frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} - \frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}\right) + \frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} + \frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}$$
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\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | | || 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | 4 / 2 / 2 2 \ |atan2\432*im(x2) + 246*im(x2)*re(x2), 324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/|| | | || \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------|| | | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------|| | | || \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------|| | | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *sin|-----------------------------------------------------------------------------------|| | \/ (432*im(x2) + 246*im(x2)*re(x2)) + \324 - 123*im (x2) + 123*re (x2) + 432*re(x2)/ *cos|-----------------------------------------------------------------------------------|| | | ||12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /| | |12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /| | | ||12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /| | |12*im(x2) \ 2 /| |18 12*re(x2) \ 2 /| | | ||--------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2) |-- + --------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2)| |--------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2) |-- + --------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2)| | ||--------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2) |-- + --------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2)| |--------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*im(x2) |-- + --------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*re(x2)| | |\ 7 7 / \7 7 7 / | \ 7 7 / \7 7 7 / | | |\ 7 7 / \7 7 7 / | \ 7 7 / \7 7 7 / | |I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | | 2 2 2 2 | 2 2 2 2 | | | 2 2 2 2 | 2 2 2 2 | \ \ im (x2) + re (x2) im (x2) + re (x2) / im (x2) + re (x2) im (x2) + re (x2) / \ \ im (x2) + re (x2) im (x2) + re (x2) / im (x2) + re (x2) im (x2) + re (x2) /
$$\left(\frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} + i \left(\frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} - \frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}\right) + \frac{\left(- \frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}\right) \left(\frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} + i \left(\frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{im}{\left(x_{2}\right)}}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}} - \frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{im}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}\right) + \frac{\left(\frac{\sqrt[4]{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)}\right)^{2} + \left(123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(246 \operatorname{re}{\left(x_{2}\right)} \operatorname{im}{\left(x_{2}\right)} + 432 \operatorname{im}{\left(x_{2}\right)},123 \left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + 432 \operatorname{re}{\left(x_{2}\right)} - 123 \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2} + 324 \right)}}{2} \right)}}{7} + \frac{12 \operatorname{re}{\left(x_{2}\right)}}{7} + \frac{18}{7}\right) \operatorname{re}{\left(x_{2}\right)}}{\left(\operatorname{re}{\left(x_{2}\right)}\right)^{2} + \left(\operatorname{im}{\left(x_{2}\right)}\right)^{2}}\right)$$
=
3/7
$$\frac{3}{7}$$
3/7