Complex Numbers with Complex Modulus form Normed Vector Space

Theorem
Let $\C$ be the set of complex numbers.

Let $\size {\, \cdot \,}$ be the complex modulus.

Then $\struct {\C, \size {\, \cdot \,}}$ is a normed vector space.

Proof
We have that:


 * Complex Numbers form Vector Space over Themselves


 * Complex Modulus is Norm

By definition, $\struct {\C, \size {\, \cdot \,}}$ is a normed vector space.