Magnitude of Projection of Complex Number on Another

Theorem
Let $z_1$ and $z_2$ denote complex numbers in vector form.

Let $\map {\pr_1} {z_1, z_2}$ denote the projection of $z_1$ on $z_2$.

Then:
 * $\cmod {\map {\pr_1} {z_1, z_2} } = \dfrac {\cmod {z_1 \circ z_2} } {\cmod {z_2} }$

where:
 * $z_1 \circ z_2$ denotes complex dot product
 * $\cmod {z_2}$ denotes complex modulus.