Equation for Perpendicular Bisector of Two Points in Complex Plane/Standard Form

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

Let $L$ be the perpendicular bisector of the straight line through $z_1$ and $z_2$ in the complex plane.

$L$ can be expressed by the equation:
 * $\map \Re {z_2 - z_1} x + \map \Im {z_2 - z_1} y = \dfrac {\cmod {z_2}^2 - \cmod {z_1}^2} 2$

Proof
Let $z_1$ and $z_2$ be represented by the points $A = \tuple {x_1, y_1}$ and $B = \tuple {x_2, y_2}$ respectively in the complex plane.

By Equation for Perpendicular Bisector of Two Points, the equation of their perpendicular bisector can be expressed as: