If we use polar coordinates \begin{eqnarray} x&=&r\cos\theta\\ y&=&r\sin\theta \end{eqnarray} to describe the complex number $z=x+iy$, we can factor out the $r$ and use Euler's formula to obtain the exponential form of the complex number $z$: \begin{eqnarray} z&=&x+iy\\ &=&r\cos\theta + i r\sin\theta\\ &=&r(\cos\theta +i\sin\theta)\\ &=&re^{i\theta} \end{eqnarray} Just as $r$ represents the distance of $z$ from the origin in the complex plane, $\theta$ represents the polar angle, measured in radians, counterclockwise from the real axis.

Add a figure of the complex plane with polar coordinates.

It is easiest to do multiplication and division of two complex numbers $z_1=r_1e^{i\theta_1}$ and $z_2 = r_2 e^{i\theta_2}$ in exponential form: \begin{eqnarray} z_1 z_2 &=& r_1 e^{i\theta_1}\, r_2 e^{i\theta_2}\\ &=& r_1 r_2 e^{i(\theta_1 + \theta_2)}\\ \frac{z_1}{ z_2} &=& r_1 e^{i\theta_1}/ r_2 e^{i\theta_2}\\ &=& \frac{r_1}{ r_2} e^{i(\theta_1 - \theta_2)} \end{eqnarray} Notice that the magnitudes of the two complex numbers multiply (or divide) whereas the angles add (or substract).