# 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.

$\blacksquare$