Difference of Complex Conjugates

Theorem
Let $z_1, z_2 \in \C$ be complex numbers.

Let $\overline z$ denote the complex conjugate of the complex number $z$.

Then:
 * $\overline {z_1 - z_2} = \overline {z_1} - \overline {z_2}$

Proof
Let $w = -z_2$.

Then: