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.

$\blacksquare$

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