# Thread: Complex numbers theory question

1. ## Complex numbers theory question

If $z = a+bi, w = c+di$ and $arg(z+w) = 90^{\circ}$ 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?

2. If you can't get "theory" questions, it's because you don't know the basic definitions! Go back and review the definitions. Don't just get a general idea of what they mean, learn them by heart. You use the precise words of definitions in proving theorems and solving problems.

Saying that a complex number has "arg 90" means that the line from the point in the complex plane to 0 make a 90 degree angle with the positive real axis and so it lies on the positive imaginary axis. That is, z+ w is pure imaginary. What does that tell you about its real part?