Reciprocal of Power of Complex Number

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

Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Let $z^n$ denote $z$ raised to the $n$th power.

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

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