Equation of Imaginary Axis in Complex Plane

Theorem
Let $\C$ be the complex plane.

Let $z \in \C$ be subject to the condition:
 * $\left\lvert{z - 1}\right\rvert = \left\lvert{z + 1}\right\rvert$

where $\left\lvert{\, \cdot \,}\right\rvert$ denotes complex modulus.

Then the locus of $z$ is the imaginary axis.

Proof
The result follows by definition of imaginary axis.