Folks,

I have $\displaystyle z=a + ib, |z|=\sqrt{a^2+b^2}$

Axiom 1: $\displaystyle |z| \ge0$

Axiom 2: $\displaystyle |z|=0$ iff $\displaystyle a=b=0$

Axiom 3:$\displaystyle | \alpha| |z|=|\alpha z|$ for $\displaystyle \alpha \in \mathbb{C}$

Axiom 4: The triangle inequality.

How do I get started on any of these axioms?

THanks