If and then which of the following is true?

a) z + w = 0

b) |z + w| = 0

c) a = -c

d) b = -d

I hate theory questions, I can't get them for some reason. Are there any properties that would help me with this question?

Here's how I interpret it, If arg(z+w) is 90 degrees, then z is perpendicular to w. I'm not sure what else to do for this kind of question. I know the answer, but I don't know why Can someone point me in the right direction?