Triangle Inequality

Definition

| z_{1} + z_{2} | \leq | z_{1} | + | z_{2} |

| z_{1} + x_{2} | \geq | | z_{1} | - | z_{2} | |

Proof:
$| z_{1} | = | z_{1} + z_{2} - z_{2} | \leq | z_{1} + z_{2} | + | z_{2} | \Rightarrow | z_{1} + z_{2} | \geq | z_{1} | - | z_{2} |$
So:

| | z_{1} | - | z_{2} | | \leq | z_{1} + z_{2} | \leq | z_{1} | + | z_{2} |