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Homework Help: Calculating angle between two complex numbers

  1. Sep 16, 2012 #1
    so I have z1 = 3 + j, z2 = -5 + 5j, z3 = z1+z2 = -2 + 6j

    the question is, show that angle(z1) and angle(z1 + z2) differ by an integer multiple of pi/2.

    I tried doing it this way
    arctan(z1/z3), but then I always end up with a number that doesn't work. I know that arctan(x) cannot equal pi/2. Is there another way t rewrite it? I computed it using matlab and it gave me pi/2.
  2. jcsd
  3. Sep 16, 2012 #2


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    Just draw the corresponding vectors ##\langle 3,1\rangle## and ##\langle -1,3\rangle## and look at their dot product.
  4. Sep 16, 2012 #3

    Filip Larsen

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    Gold Member

    Perhaps you can utilize that pi/2 means the two complex numbers, when viewed as vectors in the complex plane, must be perpendicular to each other.
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