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- La ecuación:
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Ecuación x^2+5x=36
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Ecuación 3*x=8
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Ecuación 9-7(x+3)=5-6x
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Ecuación 4x-5=3+2(x+1)
- Expresar {x} en función de y en la ecuación:
- -17*x+2*y=9
- 10*x-15*y=16
- -17*x+2*y=-4
- -2*x-19*y=3
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Expresiones idénticas
- ax^ dos -3x-a= cero
- ax al cuadrado menos 3x menos a es igual a 0
- ax en el grado dos menos 3x menos a es igual a cero
- ax2-3x-a=0
- ax²-3x-a=0
- ax en el grado 2-3x-a=0
- ax^2-3x-a=O
-
Expresiones semejantes
- ax^2+3x-a=0
- ax^2-3x+a=0
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Expresiones con funciones
- ax
- ax2+bx+с=0
- ax-|x|-|x+2|=a/2
- ax^2-7x+1=0
- ax=3x-5
- ax-12=4a-3x
ax^2-3x-a=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
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
$$b = -3$$
$$c = - a$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{\sqrt{4 a^{2} + 9} + 3}{2 a}$$
$$x_{2} = \frac{3 - \sqrt{4 a^{2} + 9}}{2 a}$$
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
True
$$b = -3$$
$$c = - a$$
, entonces
D = b^2 - 4 * a * c =
(-3)^2 - 4 * (a) * (-a) = 9 + 4*a^2
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{\sqrt{4 a^{2} + 9} + 3}{2 a}$$
$$x_{2} = \frac{3 - \sqrt{4 a^{2} + 9}}{2 a}$$
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$a x^{2} - a - 3 x = 0$$
Коэффициент при x равен
$$a$$
entonces son posibles los casos para a :
$$a < 0$$
$$a = 0$$
Consideremos todos los casos con detalles:
Con
$$a < 0$$
la ecuación será
$$- x^{2} - 3 x + 1 = 0$$
su solución
$$x = - \frac{3}{2} + \frac{\sqrt{13}}{2}$$
$$x = - \frac{\sqrt{13}}{2} - \frac{3}{2}$$
Con
$$a = 0$$
la ecuación será
$$- 3 x = 0$$
su solución
$$x = 0$$
$$a x^{2} - a - 3 x = 0$$
Коэффициент при x равен
$$a$$
entonces son posibles los casos para a :
$$a < 0$$
$$a = 0$$
Consideremos todos los casos con detalles:
Con
$$a < 0$$
la ecuación será
$$- x^{2} - 3 x + 1 = 0$$
su solución
$$x = - \frac{3}{2} + \frac{\sqrt{13}}{2}$$
$$x = - \frac{\sqrt{13}}{2} - \frac{3}{2}$$
Con
$$a = 0$$
la ecuación será
$$- 3 x = 0$$
su solución
$$x = 0$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$- a + \left(a x^{2} - 3 x\right) = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{a x^{2} - a - 3 x}{a} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{3}{a}$$
$$q = \frac{c}{a}$$
$$q = -1$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{3}{a}$$
$$x_{1} x_{2} = -1$$
$$- a + \left(a x^{2} - 3 x\right) = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{a x^{2} - a - 3 x}{a} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{3}{a}$$
$$q = \frac{c}{a}$$
$$q = -1$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{3}{a}$$
$$x_{1} x_{2} = -1$$
Gráfica
Respuesta rápida
[src]
/ / _______________________________________________ \ _______________________________________________ \ / _______________________________________________ \ _______________________________________________
| | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | / 2 / / 2 2 \\| / 2 / / 2 2 \\
| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|
| |3 - \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*im(a) \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *re(a)*sin|---------------------------------------------|| |3 - \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*re(a) \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *im(a)*sin|---------------------------------------------|
| \ \ 2 // \ 2 /| \ \ 2 // \ 2 /
x1 = I*|- ------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------
| / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \
\ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / 2*\im (a) + re (a)/ 2*\im (a) + re (a)/
$$x_{1} = \frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(- \frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) - \frac{\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}$$
/ / _______________________________________________ \ _______________________________________________ \ / _______________________________________________ \ _______________________________________________
| | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | / 2 / / 2 2 \\| / 2 / / 2 2 \\
| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|
| |3 + \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*im(a) \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *re(a)*sin|---------------------------------------------|| |3 + \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*re(a) \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *im(a)*sin|---------------------------------------------|
| \ \ 2 // \ 2 /| \ \ 2 // \ 2 /
x2 = I*|- ------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------
| / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \
\ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / 2*\im (a) + re (a)/ 2*\im (a) + re (a)/
$$x_{2} = \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(- \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}$$
x2 = (((4*re(a)^2 - 4*im(a)^2 + 9)^2 + 64*re(a)^2*im(a)^2)^(1/4)*cos(atan2(8*re(a)*im(a, 4*re(a)^2 - 4*im(a)^2 + 9)/2) + 3)*re(a)/(2*(re(a)^2 + im(a)^2)) + i*(-(((4*re(a)^2 - 4*im(a)^2 + 9)^2 + 64*re(a)^2*im(a)^2)^(1/4)*cos(atan2(8*re(a)*im(a), 4*re(a)^2 - 4*im(a)^2 + 9)/2) + 3)*im(a)/(2*(re(a)^2 + im(a)^2)) + ((4*re(a)^2 - 4*im(a)^2 + 9)^2 + 64*re(a)^2*im(a)^2)^(1/4)*sin(atan2(8*re(a)*im(a), 4*re(a)^2 - 4*im(a)^2 + 9)/2)*re(a)/(2*(re(a)^2 + im(a)^2))) + ((4*re(a)^2 - 4*im(a)^2 + 9)^2 + 64*re(a)^2*im(a)^2)^(1/4)*sin(atan2(8*re(a)*im(a), 4*re(a)^2 - 4*im(a)^2 + 9)/2)*im(a)/(2*(re(a)^2 + im(a)^2)))
Suma y producto de raíces
[src]
suma
/ / _______________________________________________ \ _______________________________________________ \ / _______________________________________________ \ _______________________________________________ / / _______________________________________________ \ _______________________________________________ \ / _______________________________________________ \ _______________________________________________ | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | / 2 / / 2 2 \\| / 2 / / 2 2 \\ | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | / 2 / / 2 2 \\| / 2 / / 2 2 \\ | | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/| | | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/| | |3 - \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*im(a) \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *re(a)*sin|---------------------------------------------|| |3 - \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*re(a) \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *im(a)*sin|---------------------------------------------| | |3 + \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*im(a) \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *re(a)*sin|---------------------------------------------|| |3 + \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*re(a) \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *im(a)*sin|---------------------------------------------| | \ \ 2 // \ 2 /| \ \ 2 // \ 2 / | \ \ 2 // \ 2 /| \ \ 2 // \ 2 / I*|- ------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------ + I*|- ------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------ | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ \ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ \ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / 2*\im (a) + re (a)/ 2*\im (a) + re (a)/
$$\left(\frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(- \frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) - \frac{\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \left(\frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(- \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right)$$
=
/ / _______________________________________________ \ _______________________________________________ \ / / _______________________________________________ \ _______________________________________________ \ / _______________________________________________ \ / _______________________________________________ \ | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| | | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| | |3 + \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*im(a) \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *re(a)*sin|---------------------------------------------|| | |3 - \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*im(a) \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *re(a)*sin|---------------------------------------------|| |3 + \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*re(a) |3 - \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*re(a) | \ \ 2 // \ 2 /| | \ \ 2 // \ 2 /| \ \ 2 // \ \ 2 // I*|- ------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------| + I*|- ------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------ | / 2 2 \ / 2 2 \ | | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ \ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / \ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / 2*\im (a) + re (a)/ 2*\im (a) + re (a)/
$$\frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(- \frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + i \left(- \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right)$$
producto
/ / / _______________________________________________ \ _______________________________________________ \ / _______________________________________________ \ _______________________________________________ \ / / / _______________________________________________ \ _______________________________________________ \ / _______________________________________________ \ _______________________________________________ \ | | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| | | | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| | 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| 4 / / 2 2 \ 2 2 |atan2\8*im(a)*re(a), 9 - 4*im (a) + 4*re (a)/|| | | |3 - \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*im(a) \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *re(a)*sin|---------------------------------------------|| |3 - \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*re(a) \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *im(a)*sin|---------------------------------------------|| | | |3 + \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*im(a) \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *re(a)*sin|---------------------------------------------|| |3 + \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *cos|---------------------------------------------||*re(a) \/ \9 - 4*im (a) + 4*re (a)/ + 64*im (a)*re (a) *im(a)*sin|---------------------------------------------|| | | \ \ 2 // \ 2 /| \ \ 2 // \ 2 /| | | \ \ 2 // \ 2 /| \ \ 2 // \ 2 /| |I*|- ------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------|*|I*|- ------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------| | | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ | | | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ | \ \ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / \ \ 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ / 2*\im (a) + re (a)/ 2*\im (a) + re (a)/ /
$$\left(\frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(- \frac{\left(- \sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) - \frac{\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) \left(\frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(- \frac{\left(\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + 3\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + \frac{\sqrt[4]{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2} + 64 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right)$$
=
-1
$$-1$$
-1