Could someone explain why you multiply the lengths and add the angles when multiplying polar coordinates?
I tried multiplying the polar forms ($r_1\left(\cos\theta_1 + i\sin\theta_1\right)\cdot r_2\left(\cos\theta_2 + i\sin\theta_2\right)$), and expanding/factoring the result, and end up multiplying the lengths but can't seem to come to an equation where you add the angles.