Triangle Inequality for Complex Numbers/Corollary 1

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

Let $\cmod z$ be the modulus of $z$.

Then:
 * $\cmod {z_1 + z_2} \ge \cmod {z_1} - \cmod {z_2}$

Proof
Let $z_3 := z_1 + z_2$.

Then: