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- La ecuación:
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Ecuación 3*x^2-x+2=0
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Ecuación 1-x/2=x/3
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Ecuación 3*x^2-9=0
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Ecuación 0,084:(6,2-x)=1,2
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- -17*x+2*y=9
- 10*x-15*y=16
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Expresiones idénticas
- h=sqrt(a^ dos - dos *a*b+b^ dos -((a+b)/ dos))
- h es igual a raíz cuadrada de (a al cuadrado menos 2 multiplicar por a multiplicar por b más b al cuadrado menos ((a más b) dividir por 2))
- h es igual a raíz cuadrada de (a en el grado dos menos dos multiplicar por a multiplicar por b más b en el grado dos menos ((a más b) dividir por dos))
- h=√(a^2-2*a*b+b^2-((a+b)/2))
- h=sqrt(a2-2*a*b+b2-((a+b)/2))
- h=sqrta2-2*a*b+b2-a+b/2
- h=sqrt(a²-2*a*b+b²-((a+b)/2))
- h=sqrt(a en el grado 2-2*a*b+b en el grado 2-((a+b)/2))
- h=sqrt(a^2-2ab+b^2-((a+b)/2))
- h=sqrt(a2-2ab+b2-((a+b)/2))
- h=sqrta2-2ab+b2-a+b/2
- h=sqrta^2-2ab+b^2-a+b/2
- h=sqrt(a^2-2*a*b+b^2-((a+b) dividir por 2))
-
Expresiones semejantes
- h=sqrt(a^2-2*a*b+b^2-((a-b)/2))
- h=sqrt(a^2-2*a*b-b^2-((a+b)/2))
- h=sqrt(a^2+2*a*b+b^2-((a+b)/2))
- h=sqrt(a^2-2*a*b+b^2+((a+b)/2))
-
Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x+2)-sqrt(x-6)=2
- sqrt(56-x)=-x
- sqrt(x-2)+sqrt(4-x)=sqrt(6-x)
- sqrt(4+2x−x^2)=x−2.
- sqrt(x+4)=sqrt3x
h=sqrt(a^2-2*a*b+b^2-((a+b)/2)) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
_________________________
/ 2 2 a + b
h = / a - 2*a*b + b - -----
\/ 2
$$h = \sqrt{- \frac{a + b}{2} + \left(b^{2} + \left(a^{2} - 2 a b\right)\right)}$$
Solución detallada
Tenemos la ecuación:
$$h = \sqrt{- \frac{a + b}{2} + \left(b^{2} + \left(a^{2} - 2 a b\right)\right)}$$
cambiamos:
$$h = \frac{\sqrt{4 a^{2} - 8 a b - 2 a + 4 b^{2} - 2 b}}{2}$$
Abrimos los paréntesis en el miembro derecho de la ecuación
Sumamos los términos semejantes en el miembro derecho de la ecuación:
Obtenemos la respuesta: h = sqrt(-2*a - 2*b + 4*a^2 + 4*b^2 - 8*a*b)/2
$$h = \sqrt{- \frac{a + b}{2} + \left(b^{2} + \left(a^{2} - 2 a b\right)\right)}$$
cambiamos:
$$h = \frac{\sqrt{4 a^{2} - 8 a b - 2 a + 4 b^{2} - 2 b}}{2}$$
Abrimos los paréntesis en el miembro derecho de la ecuación
h = sqrt-2*a/2+2*b/2+4*a/2+2/2+4*b/2+2/2+8*a*b/2
Sumamos los términos semejantes en el miembro derecho de la ecuación:
h = sqrt(-2*a - 2*b + 4*a^2 + 4*b^2 - 8*a*b)/2
Obtenemos la respuesta: h = sqrt(-2*a - 2*b + 4*a^2 + 4*b^2 - 8*a*b)/2
Gráfica
Respuesta rápida
[src]
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/ 2 / / 2 2 2 2 \\ / 2 / / 2 2 2 2 \\
4 / 2 / 2 2 2 2 \ |atan2\-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b), -8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/| 4 / 2 / 2 2 2 2 \ |atan2\-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b), -8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/|
\/ (-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b)) + \-8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/ *cos|-------------------------------------------------------------------------------------------------------------------------------------------------| I*\/ (-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b)) + \-8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/ *sin|-------------------------------------------------------------------------------------------------------------------------------------------------|
\ 2 / \ 2 /
h1 = -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$h_{1} = \frac{i \sqrt[4]{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)}}{2}$$
h1 = i*((8*re(a)*im(a) + 8*re(b)*im(b) - 2*im(a) - 2*im(b) - 8*im(a*b))^2 + (4*re(a)^2 - 2*re(a) + 4*re(b)^2 - 2*re(b) - 8*re(a*b) - 4*im(a)^2 - 4*im(b)^2)^2)^(1/4)*sin(atan2(8*re(a)*im(a) + 8*re(b)*im(b) - 2*im(a) - 2*im(b) - 8*im(a*b, 4*re(a)^2 - 2*re(a) + 4*re(b)^2 - 2*re(b) - 8*re(a*b) - 4*im(a)^2 - 4*im(b)^2)/2)/2 + ((8*re(a)*im(a) + 8*re(b)*im(b) - 2*im(a) - 2*im(b) - 8*im(a*b))^2 + (4*re(a)^2 - 2*re(a) + 4*re(b)^2 - 2*re(b) - 8*re(a*b) - 4*im(a)^2 - 4*im(b)^2)^2)^(1/4)*cos(atan2(8*re(a)*im(a) + 8*re(b)*im(b) - 2*im(a) - 2*im(b) - 8*im(a*b), 4*re(a)^2 - 2*re(a) + 4*re(b)^2 - 2*re(b) - 8*re(a*b) - 4*im(a)^2 - 4*im(b)^2)/2)/2)
Suma y producto de raíces
[src]
suma
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/ 2 / / 2 2 2 2 \\ / 2 / / 2 2 2 2 \\
4 / 2 / 2 2 2 2 \ |atan2\-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b), -8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/| 4 / 2 / 2 2 2 2 \ |atan2\-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b), -8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/|
\/ (-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b)) + \-8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/ *cos|-------------------------------------------------------------------------------------------------------------------------------------------------| I*\/ (-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b)) + \-8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/ *sin|-------------------------------------------------------------------------------------------------------------------------------------------------|
\ 2 / \ 2 /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{i \sqrt[4]{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)}}{2}$$
=
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/ 2 / / 2 2 2 2 \\ / 2 / / 2 2 2 2 \\
4 / 2 / 2 2 2 2 \ |atan2\-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b), -8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/| 4 / 2 / 2 2 2 2 \ |atan2\-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b), -8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/|
\/ (-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b)) + \-8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/ *cos|-------------------------------------------------------------------------------------------------------------------------------------------------| I*\/ (-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b)) + \-8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/ *sin|-------------------------------------------------------------------------------------------------------------------------------------------------|
\ 2 / \ 2 /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{i \sqrt[4]{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)}}{2}$$
producto
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/ 2 / / 2 2 2 2 \\ / 2 / / 2 2 2 2 \\
4 / 2 / 2 2 2 2 \ |atan2\-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b), -8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/| 4 / 2 / 2 2 2 2 \ |atan2\-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b), -8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/|
\/ (-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b)) + \-8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/ *cos|-------------------------------------------------------------------------------------------------------------------------------------------------| I*\/ (-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b)) + \-8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/ *sin|-------------------------------------------------------------------------------------------------------------------------------------------------|
\ 2 / \ 2 /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{i \sqrt[4]{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2} \right)}}{2}$$
=
/ 2 2 2 2 \
___________________________________________________________________________________________________________________________________________ I*atan2\-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b), -8*re(a*b) - 4*im (a) - 4*im (b) - 2*re(a) - 2*re(b) + 4*re (a) + 4*re (b)/
/ 2 ---------------------------------------------------------------------------------------------------------------------------------------------------
___ 4 / 2 / 2 2 2 2 \ 2
\/ 2 *\/ (4*im(a*b) - 4*im(a)*re(a) - 4*im(b)*re(b) + im(a) + im(b)) + \- 2*re (a) - 2*re (b) + 2*im (a) + 2*im (b) + 4*re(a*b) + re(a) + re(b)/ *e
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
$$\frac{\sqrt{2} \sqrt[4]{\left(- 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(b\right)} + 4 \operatorname{im}{\left(a b\right)}\right)^{2} + \left(- 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \operatorname{re}{\left(a\right)} - 2 \left(\operatorname{re}{\left(b\right)}\right)^{2} + \operatorname{re}{\left(b\right)} + 4 \operatorname{re}{\left(a b\right)} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(b\right)}\right)^{2}\right)^{2}} e^{\frac{i \operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 8 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} - 2 \operatorname{im}{\left(a\right)} - 2 \operatorname{im}{\left(b\right)} - 8 \operatorname{im}{\left(a b\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{re}{\left(b\right)}\right)^{2} - 2 \operatorname{re}{\left(b\right)} - 8 \operatorname{re}{\left(a b\right)} - 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(b\right)}\right)^{2} \right)}}{2}}}{2}$$
sqrt(2)*((4*im(a*b) - 4*im(a)*re(a) - 4*im(b)*re(b) + im(a) + im(b))^2 + (-2*re(a)^2 - 2*re(b)^2 + 2*im(a)^2 + 2*im(b)^2 + 4*re(a*b) + re(a) + re(b))^2)^(1/4)*exp(i*atan2(-8*im(a*b) - 2*im(a) - 2*im(b) + 8*im(a)*re(a) + 8*im(b)*re(b), -8*re(a*b) - 4*im(a)^2 - 4*im(b)^2 - 2*re(a) - 2*re(b) + 4*re(a)^2 + 4*re(b)^2)/2)/2