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Expresiones idénticas
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Expresiones semejantes
- 48*a^2*x+8*a^2+4*x-4=33*a*x-33*a
- 48*a^2*x-8*a^2-4*x-4=33*a*x-33*a
- 48*a^2*x-8*a^2+4*x-4=33*a*x+33*a
- 48*a^2*x-8*a^2+4*x+4=33*a*x-33*a
48*a^2*x-8*a^2+4*x-4=33*a*x-33*a la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 48*a *x - 8*a + 4*x - 4 = 33*a*x - 33*a
$$\left(4 x + \left(- 8 a^{2} + 48 a^{2} x\right)\right) - 4 = - 33 a + 33 a x$$
Solución detallada
Tenemos una ecuación lineal:
Transportamos los términos libres (sin x)
del miembro izquierdo al derecho, obtenemos:
$$48 a^{2} x - 8 a^{2} + 4 x = 33 a x - 33 a + 4$$
Dividamos ambos miembros de la ecuación en (-8*a^2 + 4*x + 48*x*a^2)/x
Obtenemos la respuesta: x = (4 - 33*a + 8*a^2)/(4 - 33*a + 48*a^2)
48*a^2*x-8*a^2+4*x-4 = 33*a*x-33*a
Transportamos los términos libres (sin x)
del miembro izquierdo al derecho, obtenemos:
$$48 a^{2} x - 8 a^{2} + 4 x = 33 a x - 33 a + 4$$
Dividamos ambos miembros de la ecuación en (-8*a^2 + 4*x + 48*x*a^2)/x
x = 4 - 33*a + 33*a*x / ((-8*a^2 + 4*x + 48*x*a^2)/x)
Obtenemos la respuesta: x = (4 - 33*a + 8*a^2)/(4 - 33*a + 48*a^2)
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$48 a^{2} x - 8 a^{2} + 4 x - 4 = 33 a x - 33 a$$
Коэффициент при x равен
$$48 a^{2} - 33 a + 4$$
entonces son posibles los casos para a :
$$a < \frac{11}{32} - \frac{\sqrt{321}}{96}$$
$$a = \frac{11}{32} - \frac{\sqrt{321}}{96}$$
$$a > \frac{11}{32} - \frac{\sqrt{321}}{96} \wedge a < \frac{\sqrt{321}}{96} + \frac{11}{32}$$
$$a = \frac{\sqrt{321}}{96} + \frac{11}{32}$$
Consideremos todos los casos con detalles:
Con
$$a < \frac{11}{32} - \frac{\sqrt{321}}{96}$$
la ecuación será
$$4 x - 33 x \left(- \frac{21}{32} - \frac{\sqrt{321}}{96}\right) + 48 x \left(- \frac{21}{32} - \frac{\sqrt{321}}{96}\right)^{2} - \frac{821}{32} - \frac{11 \sqrt{321}}{32} - 8 \left(- \frac{21}{32} - \frac{\sqrt{321}}{96}\right)^{2} = 0$$
su solución
$$x = \frac{80947}{126912} - \frac{1465 \sqrt{321}}{380736}$$
Con
$$a = \frac{11}{32} - \frac{\sqrt{321}}{96}$$
la ecuación será
$$- 33 x \left(\frac{11}{32} - \frac{\sqrt{321}}{96}\right) + 48 x \left(\frac{11}{32} - \frac{\sqrt{321}}{96}\right)^{2} + 4 x - \frac{11 \sqrt{321}}{32} - 8 \left(\frac{11}{32} - \frac{\sqrt{321}}{96}\right)^{2} + \frac{235}{32} = 0$$
su solución
Con
$$a > \frac{11}{32} - \frac{\sqrt{321}}{96} \wedge a < \frac{\sqrt{321}}{96} + \frac{11}{32}$$
la ecuación será
$$\frac{819}{128} - \frac{107 x}{64} = 0$$
su solución
$$x = \frac{819}{214}$$
Con
$$a = \frac{\sqrt{321}}{96} + \frac{11}{32}$$
la ecuación será
$$- 33 x \left(\frac{\sqrt{321}}{96} + \frac{11}{32}\right) + 4 x + 48 x \left(\frac{\sqrt{321}}{96} + \frac{11}{32}\right)^{2} - 8 \left(\frac{\sqrt{321}}{96} + \frac{11}{32}\right)^{2} + \frac{11 \sqrt{321}}{32} + \frac{235}{32} = 0$$
su solución
$$48 a^{2} x - 8 a^{2} + 4 x - 4 = 33 a x - 33 a$$
Коэффициент при x равен
$$48 a^{2} - 33 a + 4$$
entonces son posibles los casos para a :
$$a < \frac{11}{32} - \frac{\sqrt{321}}{96}$$
$$a = \frac{11}{32} - \frac{\sqrt{321}}{96}$$
$$a > \frac{11}{32} - \frac{\sqrt{321}}{96} \wedge a < \frac{\sqrt{321}}{96} + \frac{11}{32}$$
$$a = \frac{\sqrt{321}}{96} + \frac{11}{32}$$
Consideremos todos los casos con detalles:
Con
$$a < \frac{11}{32} - \frac{\sqrt{321}}{96}$$
la ecuación será
$$4 x - 33 x \left(- \frac{21}{32} - \frac{\sqrt{321}}{96}\right) + 48 x \left(- \frac{21}{32} - \frac{\sqrt{321}}{96}\right)^{2} - \frac{821}{32} - \frac{11 \sqrt{321}}{32} - 8 \left(- \frac{21}{32} - \frac{\sqrt{321}}{96}\right)^{2} = 0$$
su solución
$$x = \frac{80947}{126912} - \frac{1465 \sqrt{321}}{380736}$$
Con
$$a = \frac{11}{32} - \frac{\sqrt{321}}{96}$$
la ecuación será
$$- 33 x \left(\frac{11}{32} - \frac{\sqrt{321}}{96}\right) + 48 x \left(\frac{11}{32} - \frac{\sqrt{321}}{96}\right)^{2} + 4 x - \frac{11 \sqrt{321}}{32} - 8 \left(\frac{11}{32} - \frac{\sqrt{321}}{96}\right)^{2} + \frac{235}{32} = 0$$
su solución
Con
$$a > \frac{11}{32} - \frac{\sqrt{321}}{96} \wedge a < \frac{\sqrt{321}}{96} + \frac{11}{32}$$
la ecuación será
$$\frac{819}{128} - \frac{107 x}{64} = 0$$
su solución
$$x = \frac{819}{214}$$
Con
$$a = \frac{\sqrt{321}}{96} + \frac{11}{32}$$
la ecuación será
$$- 33 x \left(\frac{\sqrt{321}}{96} + \frac{11}{32}\right) + 4 x + 48 x \left(\frac{\sqrt{321}}{96} + \frac{11}{32}\right)^{2} - 8 \left(\frac{\sqrt{321}}{96} + \frac{11}{32}\right)^{2} + \frac{11 \sqrt{321}}{32} + \frac{235}{32} = 0$$
su solución
Gráfica
Respuesta rápida
[src]
/ / 2 2 \ / 2 2 \ \ / 2 2 \ / 2 2 \
| (-33*im(a) + 16*im(a)*re(a))*\4 - 48*im (a) - 33*re(a) + 48*re (a)/ (33*im(a) - 96*im(a)*re(a))*\4 - 33*re(a) - 8*im (a) + 8*re (a)/ | \4 - 48*im (a) - 33*re(a) + 48*re (a)/*\4 - 33*re(a) - 8*im (a) + 8*re (a)/ (-33*im(a) + 16*im(a)*re(a))*(33*im(a) - 96*im(a)*re(a))
x1 = I*|----------------------------------------------------------------------- + -----------------------------------------------------------------------| + --------------------------------------------------------------------------- - -----------------------------------------------------------------------
| 2 2| 2 2
| 2 / 2 2 \ 2 / 2 2 \ | 2 / 2 2 \ 2 / 2 2 \
\(-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/ (-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/ / (-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/ (-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/
$$x_{1} = - \frac{\left(- 96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 33 \operatorname{im}{\left(a\right)}\right) \left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}} + i \left(\frac{\left(- 96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 33 \operatorname{im}{\left(a\right)}\right) \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}} + \frac{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right) \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}}\right) + \frac{\left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right) \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}}$$
x1 = -(-96*re(a)*im(a) + 33*im(a))*(16*re(a)*im(a) - 33*im(a))/((96*re(a)*im(a) - 33*im(a))^2 + (48*re(a)^2 - 33*re(a) - 48*im(a)^2 + 4)^2) + i*((-96*re(a)*im(a) + 33*im(a))*(8*re(a)^2 - 33*re(a) - 8*im(a)^2 + 4)/((96*re(a)*im(a) - 33*im(a))^2 + (48*re(a)^2 - 33*re(a) - 48*im(a)^2 + 4)^2) + (16*re(a)*im(a) - 33*im(a))*(48*re(a)^2 - 33*re(a) - 48*im(a)^2 + 4)/((96*re(a)*im(a) - 33*im(a))^2 + (48*re(a)^2 - 33*re(a) - 48*im(a)^2 + 4)^2)) + (8*re(a)^2 - 33*re(a) - 8*im(a)^2 + 4)*(48*re(a)^2 - 33*re(a) - 48*im(a)^2 + 4)/((96*re(a)*im(a) - 33*im(a))^2 + (48*re(a)^2 - 33*re(a) - 48*im(a)^2 + 4)^2)
Suma y producto de raíces
[src]
suma
/ / 2 2 \ / 2 2 \ \ / 2 2 \ / 2 2 \ | (-33*im(a) + 16*im(a)*re(a))*\4 - 48*im (a) - 33*re(a) + 48*re (a)/ (33*im(a) - 96*im(a)*re(a))*\4 - 33*re(a) - 8*im (a) + 8*re (a)/ | \4 - 48*im (a) - 33*re(a) + 48*re (a)/*\4 - 33*re(a) - 8*im (a) + 8*re (a)/ (-33*im(a) + 16*im(a)*re(a))*(33*im(a) - 96*im(a)*re(a)) I*|----------------------------------------------------------------------- + -----------------------------------------------------------------------| + --------------------------------------------------------------------------- - ----------------------------------------------------------------------- | 2 2| 2 2 | 2 / 2 2 \ 2 / 2 2 \ | 2 / 2 2 \ 2 / 2 2 \ \(-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/ (-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/ / (-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/ (-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/
$$- \frac{\left(- 96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 33 \operatorname{im}{\left(a\right)}\right) \left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}} + i \left(\frac{\left(- 96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 33 \operatorname{im}{\left(a\right)}\right) \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}} + \frac{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right) \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}}\right) + \frac{\left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right) \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}}$$
=
/ / 2 2 \ / 2 2 \ \ / 2 2 \ / 2 2 \ | (-33*im(a) + 16*im(a)*re(a))*\4 - 48*im (a) - 33*re(a) + 48*re (a)/ (33*im(a) - 96*im(a)*re(a))*\4 - 33*re(a) - 8*im (a) + 8*re (a)/ | \4 - 48*im (a) - 33*re(a) + 48*re (a)/*\4 - 33*re(a) - 8*im (a) + 8*re (a)/ (-33*im(a) + 16*im(a)*re(a))*(33*im(a) - 96*im(a)*re(a)) I*|----------------------------------------------------------------------- + -----------------------------------------------------------------------| + --------------------------------------------------------------------------- - ----------------------------------------------------------------------- | 2 2| 2 2 | 2 / 2 2 \ 2 / 2 2 \ | 2 / 2 2 \ 2 / 2 2 \ \(-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/ (-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/ / (-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/ (-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/
$$- \frac{\left(- 96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 33 \operatorname{im}{\left(a\right)}\right) \left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}} + i \left(\frac{\left(- 96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 33 \operatorname{im}{\left(a\right)}\right) \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}} + \frac{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right) \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}}\right) + \frac{\left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right) \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}}$$
producto
/ / 2 2 \ / 2 2 \ \ / 2 2 \ / 2 2 \ | (-33*im(a) + 16*im(a)*re(a))*\4 - 48*im (a) - 33*re(a) + 48*re (a)/ (33*im(a) - 96*im(a)*re(a))*\4 - 33*re(a) - 8*im (a) + 8*re (a)/ | \4 - 48*im (a) - 33*re(a) + 48*re (a)/*\4 - 33*re(a) - 8*im (a) + 8*re (a)/ (-33*im(a) + 16*im(a)*re(a))*(33*im(a) - 96*im(a)*re(a)) I*|----------------------------------------------------------------------- + -----------------------------------------------------------------------| + --------------------------------------------------------------------------- - ----------------------------------------------------------------------- | 2 2| 2 2 | 2 / 2 2 \ 2 / 2 2 \ | 2 / 2 2 \ 2 / 2 2 \ \(-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/ (-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/ / (-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/ (-33*im(a) + 96*im(a)*re(a)) + \4 - 48*im (a) - 33*re(a) + 48*re (a)/
$$- \frac{\left(- 96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 33 \operatorname{im}{\left(a\right)}\right) \left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}} + i \left(\frac{\left(- 96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 33 \operatorname{im}{\left(a\right)}\right) \left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}} + \frac{\left(16 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right) \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}}\right) + \frac{\left(8 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 8 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right) \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)}{\left(96 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 33 \operatorname{im}{\left(a\right)}\right)^{2} + \left(48 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 33 \operatorname{re}{\left(a\right)} - 48 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4\right)^{2}}$$
=
3 4 4 2 2 2 2 2 3 2
16 - 1848*re (a) - 264*re(a) + 384*im (a) + 384*re (a) + 865*im (a) + 1313*re (a) - 1848*im (a)*re(a) + 768*im (a)*re (a) + 1320*I*im (a) - 320*I*im(a)*re(a) + 1320*I*re (a)*im(a)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 2 2 4 4 2 2 2
16 - 3168*re (a) - 264*re(a) + 705*im (a) + 1473*re (a) + 2304*im (a) + 2304*re (a) - 3168*im (a)*re(a) + 4608*im (a)*re (a)
$$\frac{384 \left(\operatorname{re}{\left(a\right)}\right)^{4} - 1848 \left(\operatorname{re}{\left(a\right)}\right)^{3} + 768 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1320 i \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} + 1313 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 1848 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 320 i \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 264 \operatorname{re}{\left(a\right)} + 384 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 1320 i \left(\operatorname{im}{\left(a\right)}\right)^{3} + 865 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 16}{2304 \left(\operatorname{re}{\left(a\right)}\right)^{4} - 3168 \left(\operatorname{re}{\left(a\right)}\right)^{3} + 4608 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1473 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 3168 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 264 \operatorname{re}{\left(a\right)} + 2304 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 705 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 16}$$
(16 - 1848*re(a)^3 - 264*re(a) + 384*im(a)^4 + 384*re(a)^4 + 865*im(a)^2 + 1313*re(a)^2 - 1848*im(a)^2*re(a) + 768*im(a)^2*re(a)^2 + 1320*i*im(a)^3 - 320*i*im(a)*re(a) + 1320*i*re(a)^2*im(a))/(16 - 3168*re(a)^3 - 264*re(a) + 705*im(a)^2 + 1473*re(a)^2 + 2304*im(a)^4 + 2304*re(a)^4 - 3168*im(a)^2*re(a) + 4608*im(a)^2*re(a)^2)