Absolute Value of Complex Dot Product is Commutative

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

Let $z_1 \circ z_2$ denote the (complex) dot product of $z_1$ and $z_2$.

Then:
 * $\size {z_1 \circ z_2} = \size {z_2 \circ z_1}$

where $\size {\, \cdot \,}$ denotes the absolute value function.

Proof
From Dot Product Operator is Commutative‎:
 * $z_1 \circ z_2 = z_2 \circ z_1$

The result follows trivially.