Product of Complex Numbers in Polar Form

Theorem
Let $z_1 := \left\langle{r_1, \theta_1}\right\rangle$ and $z_2 := \left\langle{r_2, \theta_2}\right\rangle$ be complex numbers expressed in polar form.

Then:
 * $z_1 z_2 = r_1 r_2 \left({\cos \left({\theta_1 + \theta_2}\right) + i \sin \left({\theta_1 + \theta_2}\right)}\right)$