Polar Form Operations

Once two complex numbers are in polar form, $z_1 = r_1(\cos\theta_1+i\sin\theta_1)$ and $z_2 = r_2(\cos\theta_2+i\sin\theta_2)$, multiplying and dividing them is just multiplying/dividing the moduli and adding/subtracting the arguments:

$z_1 z_2 = r_1 r_2\big[\cos(\theta_1+\theta_2) + i\sin(\theta_1+\theta_2)\big]$

$\frac{z_1}{z_2} = \frac{r_1}{r_2}\big[\cos(\theta_1-\theta_2) + i\sin(\theta_1-\theta_2)\big]$

Example: $r_1=2, \theta_1=30^\circ$ and $r_2=3, \theta_2=60^\circ$ gives product $6(\cos 90^\circ + i\sin 90^\circ) = 6i$.