Proof for Property of Complex Numbers Is the inequality $\lvert z_1 + z_2 \rvert \ge \lvert z_1 \rvert - \lvert z_2 \rvert$ incorrect, where $z_1$ and $z_2$ are any two complex numbers? I need an example to prove that it is. And in case it is correct, can you please give the proof? Thanks for any help.

It's correct. From the inequality:
$$||z_1|-|z_2||\leq |z_1-z_2|$$
if you substitute $z_2=-z_2$, you get:
$$||z_1|-|-z_2||\leq |z_1-(-z_2)|=|z_1+z_2|$$
and now, recall that $a\leq|a|$ for every real number $a$ to conclude:
$$|z_1|-|z_2|\leq||z_1|-|z_2||\leq |z_1+z_2|$$
