Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
-
Ecuación x^2-5x=0
-
Ecuación x^2+4=5x
- Ecuación x^4-35*x^2-36=0
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- -17*x-15*y=-17
- -6*x-10*y=19
- -9*x+11*y=9
-
Expresiones idénticas
- ax-b/a+b+bx+a/a-b=a^ dos +b^ dos /a^ dos -b^ dos
- ax menos b dividir por a más b más bx más a dividir por a menos b es igual a a al cuadrado más b al cuadrado dividir por a al cuadrado menos b al cuadrado
- ax menos b dividir por a más b más bx más a dividir por a menos b es igual a a en el grado dos más b en el grado dos dividir por a en el grado dos menos b en el grado dos
- ax-b/a+b+bx+a/a-b=a2+b2/a2-b2
- ax-b/a+b+bx+a/a-b=a²+b²/a²-b²
- ax-b/a+b+bx+a/a-b=a en el grado 2+b en el grado 2/a en el grado 2-b en el grado 2
- ax-b dividir por a+b+bx+a dividir por a-b=a^2+b^2 dividir por a^2-b^2
-
Expresiones semejantes
- ax-b/a+b+bx+a/a-b=a^2-b^2/a^2-b^2
- ax-b/a+b+bx+a/a-b=a^2+b^2/a^2+b^2
- ax-b/a+b+bx-a/a-b=a^2+b^2/a^2-b^2
- ax-b/a-b+bx+a/a-b=a^2+b^2/a^2-b^2
- ax-b/a+b+bx+a/a+b=a^2+b^2/a^2-b^2
- ax-b/a+b-bx+a/a-b=a^2+b^2/a^2-b^2
- ax+b/a+b+bx+a/a-b=a^2+b^2/a^2-b^2
-
Expresiones con funciones
- ax
- ax^2=c
- ax+by+c=0
- ax+8=a
- ax^2+2x^2+2ax+a-2-x=0
- ax=a+1+x
ax-b/a+b+bx+a/a-b=a^2+b^2/a^2-b^2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2
b a 2 b 2
a*x - - + b + b*x + - - b = a + -- - b
a a 2
a
$$- b + \left(\left(b x + \left(b + \left(a x - \frac{b}{a}\right)\right)\right) + \frac{a}{a}\right) = - b^{2} + \left(a^{2} + \frac{b^{2}}{a^{2}}\right)$$
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$a x + b x + 1 - \frac{b}{a} = a^{2} - b^{2} + \frac{b^{2}}{a^{2}}$$
Коэффициент при x равен
$$a + b$$
entonces son posibles los casos para a :
$$a < - b$$
$$a = - b$$
Consideremos todos los casos con detalles:
Con
$$a < - b$$
la ecuación será
$$b^{2} - \frac{b^{2}}{\left(- b - 1\right)^{2}} + b x - \frac{b}{- b - 1} + x \left(- b - 1\right) - \left(- b - 1\right)^{2} + 1 = 0$$
su solución
$$x = - \frac{b \left(2 b^{2} + 4 b + 1\right)}{b^{2} + 2 b + 1}$$
Con
$$a = - b$$
la ecuación será
$$1 = 0$$
su solución
no hay soluciones
$$a x + b x + 1 - \frac{b}{a} = a^{2} - b^{2} + \frac{b^{2}}{a^{2}}$$
Коэффициент при x равен
$$a + b$$
entonces son posibles los casos para a :
$$a < - b$$
$$a = - b$$
Consideremos todos los casos con detalles:
Con
$$a < - b$$
la ecuación será
$$b^{2} - \frac{b^{2}}{\left(- b - 1\right)^{2}} + b x - \frac{b}{- b - 1} + x \left(- b - 1\right) - \left(- b - 1\right)^{2} + 1 = 0$$
su solución
$$x = - \frac{b \left(2 b^{2} + 4 b + 1\right)}{b^{2} + 2 b + 1}$$
Con
$$a = - b$$
la ecuación será
$$1 = 0$$
su solución
no hay soluciones
Gráfica
Respuesta rápida
[src]
// / 2 2\ 3 3 \ / 1 \ / 2 4 4 2 2 2 / 2 2\ 2 2 \ / 1 \\ / 2 4 4 2 2 2 / 2 2\ 2 2 \ / 1 \ / / 2 2\ 3 3 \ / 1 \
x1 = I*|\- im\a *b / - 4*im (a)*re(a) - 2*im(a)*re(a) + 2*im(b)*re(b) + 4*re (a)*im(a) + im(a*b)/*re|----------| + \im (a) + im (a) + re (a) + re (b) - im (b) - re (a) - re\a *b / - 6*im (a)*re (a) + re(a*b)/*im|----------|| + \im (a) + im (a) + re (a) + re (b) - im (b) - re (a) - re\a *b / - 6*im (a)*re (a) + re(a*b)/*re|----------| - \- im\a *b / - 4*im (a)*re(a) - 2*im(a)*re(a) + 2*im(b)*re(b) + 4*re (a)*im(a) + im(a*b)/*im|----------|
| | 2 | | 2 || | 2 | | 2 |
\ \a *(a + b)/ \a *(a + b)// \a *(a + b)/ \a *(a + b)/
$$x_{1} = i \left(\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} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a b\right)} - \operatorname{im}{\left(a^{2} b^{2}\right)}\right) \operatorname{re}{\left(\frac{1}{a^{2} \left(a + b\right)}\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} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + \operatorname{re}{\left(a b\right)} - \operatorname{re}{\left(a^{2} b^{2}\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a^{2} \left(a + b\right)}\right)}\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} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a b\right)} - \operatorname{im}{\left(a^{2} b^{2}\right)}\right) \operatorname{im}{\left(\frac{1}{a^{2} \left(a + b\right)}\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} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + \operatorname{re}{\left(a b\right)} - \operatorname{re}{\left(a^{2} b^{2}\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a^{2} \left(a + b\right)}\right)}$$
x1 = i*((4*re(a)^3*im(a) - 4*re(a)*im(a)^3 - 2*re(a)*im(a) + 2*re(b)*im(b) + im(a*b) - im(a^2*b^2))*re(1/(a^2*(a + b))) + (re(a)^4 - 6*re(a)^2*im(a)^2 - re(a)^2 + re(b)^2 + re(a*b) - re(a^2*b^2) + im(a)^4 + im(a)^2 - im(b)^2)*im(1/(a^2*(a + b)))) - (4*re(a)^3*im(a) - 4*re(a)*im(a)^3 - 2*re(a)*im(a) + 2*re(b)*im(b) + im(a*b) - im(a^2*b^2))*im(1/(a^2*(a + b))) + (re(a)^4 - 6*re(a)^2*im(a)^2 - re(a)^2 + re(b)^2 + re(a*b) - re(a^2*b^2) + im(a)^4 + im(a)^2 - im(b)^2)*re(1/(a^2*(a + b)))
Suma y producto de raíces
[src]
suma
// / 2 2\ 3 3 \ / 1 \ / 2 4 4 2 2 2 / 2 2\ 2 2 \ / 1 \\ / 2 4 4 2 2 2 / 2 2\ 2 2 \ / 1 \ / / 2 2\ 3 3 \ / 1 \ I*|\- im\a *b / - 4*im (a)*re(a) - 2*im(a)*re(a) + 2*im(b)*re(b) + 4*re (a)*im(a) + im(a*b)/*re|----------| + \im (a) + im (a) + re (a) + re (b) - im (b) - re (a) - re\a *b / - 6*im (a)*re (a) + re(a*b)/*im|----------|| + \im (a) + im (a) + re (a) + re (b) - im (b) - re (a) - re\a *b / - 6*im (a)*re (a) + re(a*b)/*re|----------| - \- im\a *b / - 4*im (a)*re(a) - 2*im(a)*re(a) + 2*im(b)*re(b) + 4*re (a)*im(a) + im(a*b)/*im|----------| | | 2 | | 2 || | 2 | | 2 | \ \a *(a + b)/ \a *(a + b)// \a *(a + b)/ \a *(a + b)/
$$i \left(\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} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a b\right)} - \operatorname{im}{\left(a^{2} b^{2}\right)}\right) \operatorname{re}{\left(\frac{1}{a^{2} \left(a + b\right)}\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} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + \operatorname{re}{\left(a b\right)} - \operatorname{re}{\left(a^{2} b^{2}\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a^{2} \left(a + b\right)}\right)}\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} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a b\right)} - \operatorname{im}{\left(a^{2} b^{2}\right)}\right) \operatorname{im}{\left(\frac{1}{a^{2} \left(a + b\right)}\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} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + \operatorname{re}{\left(a b\right)} - \operatorname{re}{\left(a^{2} b^{2}\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a^{2} \left(a + b\right)}\right)}$$
=
// / 2 2\ 3 3 \ / 1 \ / 2 4 4 2 2 2 / 2 2\ 2 2 \ / 1 \\ / 2 4 4 2 2 2 / 2 2\ 2 2 \ / 1 \ / / 2 2\ 3 3 \ / 1 \ I*|\- im\a *b / - 4*im (a)*re(a) - 2*im(a)*re(a) + 2*im(b)*re(b) + 4*re (a)*im(a) + im(a*b)/*re|----------| + \im (a) + im (a) + re (a) + re (b) - im (b) - re (a) - re\a *b / - 6*im (a)*re (a) + re(a*b)/*im|----------|| + \im (a) + im (a) + re (a) + re (b) - im (b) - re (a) - re\a *b / - 6*im (a)*re (a) + re(a*b)/*re|----------| - \- im\a *b / - 4*im (a)*re(a) - 2*im(a)*re(a) + 2*im(b)*re(b) + 4*re (a)*im(a) + im(a*b)/*im|----------| | | 2 | | 2 || | 2 | | 2 | \ \a *(a + b)/ \a *(a + b)// \a *(a + b)/ \a *(a + b)/
$$i \left(\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} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a b\right)} - \operatorname{im}{\left(a^{2} b^{2}\right)}\right) \operatorname{re}{\left(\frac{1}{a^{2} \left(a + b\right)}\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} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + \operatorname{re}{\left(a b\right)} - \operatorname{re}{\left(a^{2} b^{2}\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a^{2} \left(a + b\right)}\right)}\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} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a b\right)} - \operatorname{im}{\left(a^{2} b^{2}\right)}\right) \operatorname{im}{\left(\frac{1}{a^{2} \left(a + b\right)}\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} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + \operatorname{re}{\left(a b\right)} - \operatorname{re}{\left(a^{2} b^{2}\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a^{2} \left(a + b\right)}\right)}$$
producto
// / 2 2\ 3 3 \ / 1 \ / 2 4 4 2 2 2 / 2 2\ 2 2 \ / 1 \\ / 2 4 4 2 2 2 / 2 2\ 2 2 \ / 1 \ / / 2 2\ 3 3 \ / 1 \ I*|\- im\a *b / - 4*im (a)*re(a) - 2*im(a)*re(a) + 2*im(b)*re(b) + 4*re (a)*im(a) + im(a*b)/*re|----------| + \im (a) + im (a) + re (a) + re (b) - im (b) - re (a) - re\a *b / - 6*im (a)*re (a) + re(a*b)/*im|----------|| + \im (a) + im (a) + re (a) + re (b) - im (b) - re (a) - re\a *b / - 6*im (a)*re (a) + re(a*b)/*re|----------| - \- im\a *b / - 4*im (a)*re(a) - 2*im(a)*re(a) + 2*im(b)*re(b) + 4*re (a)*im(a) + im(a*b)/*im|----------| | | 2 | | 2 || | 2 | | 2 | \ \a *(a + b)/ \a *(a + b)// \a *(a + b)/ \a *(a + b)/
$$i \left(\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} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a b\right)} - \operatorname{im}{\left(a^{2} b^{2}\right)}\right) \operatorname{re}{\left(\frac{1}{a^{2} \left(a + b\right)}\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} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + \operatorname{re}{\left(a b\right)} - \operatorname{re}{\left(a^{2} b^{2}\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a^{2} \left(a + b\right)}\right)}\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} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a b\right)} - \operatorname{im}{\left(a^{2} b^{2}\right)}\right) \operatorname{im}{\left(\frac{1}{a^{2} \left(a + b\right)}\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} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + \operatorname{re}{\left(a b\right)} - \operatorname{re}{\left(a^{2} b^{2}\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a^{2} \left(a + b\right)}\right)}$$
=
// / 2 2\ 3 3 \ / 1 \ / 2 4 4 2 2 2 / 2 2\ 2 2 \ / 1 \\ / 2 4 4 2 2 2 / 2 2\ 2 2 \ / 1 \ / / 2 2\ 3 3 \ / 1 \ I*|\- im\a *b / - 4*im (a)*re(a) - 2*im(a)*re(a) + 2*im(b)*re(b) + 4*re (a)*im(a) + im(a*b)/*re|----------| + \im (a) + im (a) + re (a) + re (b) - im (b) - re (a) - re\a *b / - 6*im (a)*re (a) + re(a*b)/*im|----------|| + \im (a) + im (a) + re (a) + re (b) - im (b) - re (a) - re\a *b / - 6*im (a)*re (a) + re(a*b)/*re|----------| - \- im\a *b / - 4*im (a)*re(a) - 2*im(a)*re(a) + 2*im(b)*re(b) + 4*re (a)*im(a) + im(a*b)/*im|----------| | | 2 | | 2 || | 2 | | 2 | \ \a *(a + b)/ \a *(a + b)// \a *(a + b)/ \a *(a + b)/
$$i \left(\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} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a b\right)} - \operatorname{im}{\left(a^{2} b^{2}\right)}\right) \operatorname{re}{\left(\frac{1}{a^{2} \left(a + b\right)}\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} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + \operatorname{re}{\left(a b\right)} - \operatorname{re}{\left(a^{2} b^{2}\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{1}{a^{2} \left(a + b\right)}\right)}\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} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(b\right)} \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(a b\right)} - \operatorname{im}{\left(a^{2} b^{2}\right)}\right) \operatorname{im}{\left(\frac{1}{a^{2} \left(a + b\right)}\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} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(b\right)}\right)^{2} + \operatorname{re}{\left(a b\right)} - \operatorname{re}{\left(a^{2} b^{2}\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(b\right)}\right)^{2}\right) \operatorname{re}{\left(\frac{1}{a^{2} \left(a + b\right)}\right)}$$
i*((-im(a^2*b^2) - 4*im(a)^3*re(a) - 2*im(a)*re(a) + 2*im(b)*re(b) + 4*re(a)^3*im(a) + im(a*b))*re(1/(a^2*(a + b))) + (im(a)^2 + im(a)^4 + re(a)^4 + re(b)^2 - im(b)^2 - re(a)^2 - re(a^2*b^2) - 6*im(a)^2*re(a)^2 + re(a*b))*im(1/(a^2*(a + b)))) + (im(a)^2 + im(a)^4 + re(a)^4 + re(b)^2 - im(b)^2 - re(a)^2 - re(a^2*b^2) - 6*im(a)^2*re(a)^2 + re(a*b))*re(1/(a^2*(a + b))) - (-im(a^2*b^2) - 4*im(a)^3*re(a) - 2*im(a)*re(a) + 2*im(b)*re(b) + 4*re(a)^3*im(a) + im(a*b))*im(1/(a^2*(a + b)))