# Complex numbers theory question

• Nov 27th 2009, 02:16 AM
swtdelicaterose
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?
• Nov 27th 2009, 04:22 AM
HallsofIvy
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?