Product of Complex Numbers in Exponential Form

Theorem
Let $z_1 := r_1 e^{i \theta_1}$ and $z_2 := r_2 e^{i \theta_2}$ be complex numbers expressed in exponential form.

Then:
 * $z_1 z_2 = r_1 r_2 e^{i \paren {\theta_1 + \theta_2} }$