Consider the complex numbers in the picture below: Let $S$ be the set of all complex numbers $z$ satisfying \[|w+z| = |w| + |z|\]for the complex number $w$ above. Which of the complex numbers in the list \[s, t, u, v, w\]are in set $S$? Answer in any order you like, separating the list by commas.
If you want help with knowing where you went wrong then you should post what you have tried to do yourself and ask specific questions.
Also, if it is a direct AOPS question you should not post it here. Especially not in its entirity.
He's right. You gotta ask specific questions and not post the whole problem .