Reciprocal of Complex Number in terms of Conjugate and Modulus

Theorem
Let $z \in \C$ be a complex number.

The reciprocal of $z$ can be expressed as:
 * $\dfrac 1 z = \dfrac {\overline z} {\cmod z^2}$

where:
 * $\overline z$ denotes the complex conjugate of $z$
 * $\cmod z^2$ denotes the modulus of $z$.

Proof
Let $z$ be defined as:
 * $z = a = i b$

Then: