Product of Complex Number with Conjugate in Exponential Form

Theorem
Let $z_1$ and $z_2$ be complex numbers.

Then:
 * $\overline {z_1} z_2 = \left\vert{z_1}\right\vert \, \left\vert{z_1}\right\vert e^{i \theta}$

where:
 * $\overline {z_1}$ denotes the complex conjugate of $z_1$
 * $\left\vert{z_1}\right\vert$ denotes the complex modulus of $z_1$
 * $\theta$ denotes the angle from $z_1$ to $z_2$, measured in the positive direction.