Product of Complex Numbers in Polar Form

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

Then:
 * $z_1 z_2 = r_1 r_2 \paren {\map \cos {\theta_1 + \theta_2} + i \, \map \sin {\theta_1 + \theta_2} }$