Real part of a quotient Is there some fast way to know the real part of a quotient?
$$\Re\left(\frac{z_1}{z_2}\right)$$
$z_i\in \mathbb{C}$

If you don't have $z_1$ and $z_2$ in a "nice" form eg some of the values of $e^{i\theta}$ for various $\theta$, you could use $1/2(z+\bar{z})=\Re{(z)}$.
So you'd get:
$\Re(\frac{z_1}{z_2})=\frac{z_1\bar{z_2}+\bar{z_1}z_2}{2z_2\bar{z_2}}$
for
$z_1=r_1e^{i\theta_1}$
$z_2=r_2e^{i\theta_2}$
$\Re(\frac{z_1}{z_2})=\frac{r_1}{r_2}cos(\theta_1-\theta_2)$
Just as an alternative, although I suspect you wanted something like user130512's post.
