Properties of Norm on Division Ring/Norm of Power Equals Unity

Theorem
Let $\struct {R, +, \circ}$ be a division ring with zero $0_R$ and unity $1_R$.

Let $\norm{\,\cdot\,}$ be a norm on $R$.

Let $x \in R$

Then:
 * $\forall n \in \N_{\gt 0}: \norm{x^{n}} = 1 \implies {\norm{x}} = 1$