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Math Help - Complex numbers theory question

  1. #1
    Junior Member
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    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?
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  2. #2
    MHF Contributor

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    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?
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