Complex Numbers with Complex Modulus form Normed Vector Space
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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:
By definition, $\struct {\C, \size {\, \cdot \,}}$ is a normed vector space.
$\blacksquare$
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