Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
-
Ecuación x^2+4=5x
-
Ecuación x(x^2+2x+1)=6(x+1)
-
Ecuación 4x+1=-3x+15
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 13*x-12*y=19
- -9*x+11*y=9
- -4*x-8*y=-20
-
Expresiones idénticas
- sqrt(x^ dos +7x- ocho)+sqrt(x^ dos - uno)=a*(sqrt(x- uno))
- raíz cuadrada de (x al cuadrado más 7x menos 8) más raíz cuadrada de (x al cuadrado menos 1) es igual a a multiplicar por ( raíz cuadrada de (x menos 1))
- raíz cuadrada de (x en el grado dos más 7x menos ocho) más raíz cuadrada de (x en el grado dos menos uno) es igual a a multiplicar por ( raíz cuadrada de (x menos uno))
- √(x^2+7x-8)+√(x^2-1)=a*(√(x-1))
- sqrt(x2+7x-8)+sqrt(x2-1)=a*(sqrt(x-1))
- sqrtx2+7x-8+sqrtx2-1=a*sqrtx-1
- sqrt(x²+7x-8)+sqrt(x²-1)=a*(sqrt(x-1))
- sqrt(x en el grado 2+7x-8)+sqrt(x en el grado 2-1)=a*(sqrt(x-1))
- sqrt(x^2+7x-8)+sqrt(x^2-1)=a(sqrt(x-1))
- sqrt(x2+7x-8)+sqrt(x2-1)=a(sqrt(x-1))
- sqrtx2+7x-8+sqrtx2-1=asqrtx-1
- sqrtx^2+7x-8+sqrtx^2-1=asqrtx-1
-
Expresiones semejantes
- sqrt(x^2+7x-8)+sqrt(x^2-1)=a*(sqrt(x+1))
- sqrt(x^2+7x-8)+sqrt(x^2+1)=a*(sqrt(x-1))
- sqrt(x^2+7x+8)+sqrt(x^2-1)=a*(sqrt(x-1))
- sqrt(x^2+7x-8)-sqrt(x^2-1)=a*(sqrt(x-1))
- sqrt(x^2-7x-8)+sqrt(x^2-1)=a*(sqrt(x-1))
-
Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x-1)=x-3
- sqrt(x+6)=x
- sqrt(16-4*x)=2
- sqrt(12-x)=x
- sqrt(5/(15-x))=1
- Raíz cuadrada sqrt
- sqrt(x-1)=x-3
- sqrt(x+6)=x
- sqrt(16-4*x)=2
- sqrt(12-x)=x
- sqrt(5/(15-x))=1
- Raíz cuadrada sqrt
- sqrt(x-1)=x-3
- sqrt(x+6)=x
- sqrt(16-4*x)=2
- sqrt(12-x)=x
- sqrt(5/(15-x))=1
sqrt(x^2+7x-8)+sqrt(x^2-1)=a*(sqrt(x-1)) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
______________ ________ / 2 / 2 _______ \/ x + 7*x - 8 + \/ x - 1 = a*\/ x - 1
$$\sqrt{x^{2} - 1} + \sqrt{\left(x^{2} + 7 x\right) - 8} = a \sqrt{x - 1}$$
Gráfica
Suma y producto de raíces
[src]
suma
// 2 2 \ / 4 4 2 2 2 2 \ \ / 2 2 \ / 3 3 \
|| im (a) re (a) | / 3 3 \ \49 + im (a) + re (a) - 18*re (a) + 18*im (a) - 6*im (a)*re (a)/*im(a)*re(a)| | im (a) re (a) | / 4 4 2 2 2 2 \ \-36*im(a)*re(a) - 4*im (a)*re(a) + 4*re (a)*im(a)/*im(a)*re(a)
1 + I*||- -------------------- + --------------------|*\-36*im(a)*re(a) - 4*im (a)*re(a) + 4*re (a)*im(a)/ - ----------------------------------------------------------------------------| + |- -------------------- + --------------------|*\49 + im (a) + re (a) - 18*re (a) + 18*im (a) - 6*im (a)*re (a)/ + ---------------------------------------------------------------
|| 2 2| 2 | | 2 2| 2
|| / 2 2 \ / 2 2 \ | / 2 2 \ | | / 2 2 \ / 2 2 \ | / 2 2 \
\\ 4*\im (a) + re (a)/ 4*\im (a) + re (a)/ / 2*\im (a) + re (a)/ / \ 4*\im (a) + re (a)/ 4*\im (a) + re (a)/ / 2*\im (a) + re (a)/
$$\left(i \left(\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 36 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) - \frac{\left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 18 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 18 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right) \operatorname{re}{\left(a\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}}\right) + \left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 18 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 18 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right) + \frac{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 36 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\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}}\right) + 1$$
=
// 2 2 \ / 4 4 2 2 2 2 \ \ / 2 2 \ / 3 3 \
|| im (a) re (a) | / 3 3 \ \49 + im (a) + re (a) - 18*re (a) + 18*im (a) - 6*im (a)*re (a)/*im(a)*re(a)| | im (a) re (a) | / 4 4 2 2 2 2 \ \-36*im(a)*re(a) - 4*im (a)*re(a) + 4*re (a)*im(a)/*im(a)*re(a)
1 + I*||- -------------------- + --------------------|*\-36*im(a)*re(a) - 4*im (a)*re(a) + 4*re (a)*im(a)/ - ----------------------------------------------------------------------------| + |- -------------------- + --------------------|*\49 + im (a) + re (a) - 18*re (a) + 18*im (a) - 6*im (a)*re (a)/ + ---------------------------------------------------------------
|| 2 2| 2 | | 2 2| 2
|| / 2 2 \ / 2 2 \ | / 2 2 \ | | / 2 2 \ / 2 2 \ | / 2 2 \
\\ 4*\im (a) + re (a)/ 4*\im (a) + re (a)/ / 2*\im (a) + re (a)/ / \ 4*\im (a) + re (a)/ 4*\im (a) + re (a)/ / 2*\im (a) + re (a)/
$$i \left(\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 36 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) - \frac{\left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 18 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 18 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right) \operatorname{re}{\left(a\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}}\right) + \left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 18 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 18 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right) + 1 + \frac{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 36 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\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}}$$
producto
// 2 2 \ / 4 4 2 2 2 2 \ \ / 2 2 \ / 3 3 \ || im (a) re (a) | / 3 3 \ \49 + im (a) + re (a) - 18*re (a) + 18*im (a) - 6*im (a)*re (a)/*im(a)*re(a)| | im (a) re (a) | / 4 4 2 2 2 2 \ \-36*im(a)*re(a) - 4*im (a)*re(a) + 4*re (a)*im(a)/*im(a)*re(a) I*||- -------------------- + --------------------|*\-36*im(a)*re(a) - 4*im (a)*re(a) + 4*re (a)*im(a)/ - ----------------------------------------------------------------------------| + |- -------------------- + --------------------|*\49 + im (a) + re (a) - 18*re (a) + 18*im (a) - 6*im (a)*re (a)/ + --------------------------------------------------------------- || 2 2| 2 | | 2 2| 2 || / 2 2 \ / 2 2 \ | / 2 2 \ | | / 2 2 \ / 2 2 \ | / 2 2 \ \\ 4*\im (a) + re (a)/ 4*\im (a) + re (a)/ / 2*\im (a) + re (a)/ / \ 4*\im (a) + re (a)/ 4*\im (a) + re (a)/ / 2*\im (a) + re (a)/
$$i \left(\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 36 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) - \frac{\left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 18 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 18 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right) \operatorname{re}{\left(a\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}}\right) + \left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 18 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 18 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right) + \frac{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 36 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\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}}$$
=
6 6 2 4 4 2 2 4 4 2 2 2 5 5 3 3
re (a) - im (a) - 49*im (a) - 18*im (a) - 18*re (a) + 49*re (a) + im (a)*re (a) - im (a)*re (a) - 36*im (a)*re (a) - 98*I*im(a)*re(a) + 2*I*im (a)*re(a) + 2*I*re (a)*im(a) + 4*I*im (a)*re (a)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 4 4 2 2 \
4*\im (a) + re (a) + 2*im (a)*re (a)/
$$\frac{\left(\operatorname{re}{\left(a\right)}\right)^{6} + 2 i \left(\operatorname{re}{\left(a\right)}\right)^{5} \operatorname{im}{\left(a\right)} + \left(\operatorname{re}{\left(a\right)}\right)^{4} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 18 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 4 i \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{4} - 36 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 i \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{5} - 98 i \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{6} - 18 \left(\operatorname{im}{\left(a\right)}\right)^{4} - 49 \left(\operatorname{im}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)}$$
(re(a)^6 - im(a)^6 - 49*im(a)^2 - 18*im(a)^4 - 18*re(a)^4 + 49*re(a)^2 + im(a)^2*re(a)^4 - im(a)^4*re(a)^2 - 36*im(a)^2*re(a)^2 - 98*i*im(a)*re(a) + 2*i*im(a)^5*re(a) + 2*i*re(a)^5*im(a) + 4*i*im(a)^3*re(a)^3)/(4*(im(a)^4 + re(a)^4 + 2*im(a)^2*re(a)^2))
Respuesta rápida
[src]
x1 = 1
$$x_{1} = 1$$
// 2 2 \ / 4 4 2 2 2 2 \ \ / 2 2 \ / 3 3 \
|| im (a) re (a) | / 3 3 \ \49 + im (a) + re (a) - 18*re (a) + 18*im (a) - 6*im (a)*re (a)/*im(a)*re(a)| | im (a) re (a) | / 4 4 2 2 2 2 \ \-36*im(a)*re(a) - 4*im (a)*re(a) + 4*re (a)*im(a)/*im(a)*re(a)
x2 = I*||- -------------------- + --------------------|*\-36*im(a)*re(a) - 4*im (a)*re(a) + 4*re (a)*im(a)/ - ----------------------------------------------------------------------------| + |- -------------------- + --------------------|*\49 + im (a) + re (a) - 18*re (a) + 18*im (a) - 6*im (a)*re (a)/ + ---------------------------------------------------------------
|| 2 2| 2 | | 2 2| 2
|| / 2 2 \ / 2 2 \ | / 2 2 \ | | / 2 2 \ / 2 2 \ | / 2 2 \
\\ 4*\im (a) + re (a)/ 4*\im (a) + re (a)/ / 2*\im (a) + re (a)/ / \ 4*\im (a) + re (a)/ 4*\im (a) + re (a)/ / 2*\im (a) + re (a)/
$$x_{2} = i \left(\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 36 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) - \frac{\left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 18 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 18 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right) \operatorname{re}{\left(a\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}}\right) + \left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{4 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 18 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 18 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 49\right) + \frac{\left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 36 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\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}}$$
x2 = i*((re(a)^2/(4*(re(a)^2 + im(a)^2)^2) - im(a)^2/(4*(re(a)^2 + im(a)^2)^2))*(4*re(a)^3*im(a) - 4*re(a)*im(a)^3 - 36*re(a)*im(a)) - (re(a)^4 - 6*re(a)^2*im(a)^2 - 18*re(a)^2 + im(a)^4 + 18*im(a)^2 + 49)*re(a)*im(a)/(2*(re(a)^2 + im(a)^2)^2)) + (re(a)^2/(4*(re(a)^2 + im(a)^2)^2) - im(a)^2/(4*(re(a)^2 + im(a)^2)^2))*(re(a)^4 - 6*re(a)^2*im(a)^2 - 18*re(a)^2 + im(a)^4 + 18*im(a)^2 + 49) + (4*re(a)^3*im(a) - 4*re(a)*im(a)^3 - 36*re(a)*im(a))*re(a)*im(a)/(2*(re(a)^2 + im(a)^2)^2)