Complex Modulus is Norm

Theorem

The complex modulus is a norm on the set of complex numbers $\C$.

Proof

We prove the norm axioms.

Positive Definiteness

This is demonstrated in:

Complex Modulus equals Zero iff Zero

Complex Modulus is Non-Negative

$\Box$

Multiplicativity

Follows from Modulus of Product.

$\Box$

Triangle Inequality

Follows from Triangle Inequality for Complex Numbers.

$\blacksquare$