Triangle Inequality for Complex Numbers/Corollary 1

Theorem
Let $z_1, z_2 \in \C$ be complex numbers.

Let $\left\vert{z}\right\vert$ be the modulus of $z$.

Then:
 * $\left\vert{z_1 + z_2}\right\vert \ge \left\vert{z_1}\right\vert - \left\vert{z_2}\right\vert$

Proof
Let $z_3 := z_1 + z_2$.

Then: