Calculating angle between two complex numbers

  • #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.
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  • #2
Just draw the corresponding vectors ##\langle 3,1\rangle## and ##\langle -1,3\rangle## and look at their dot product.
  • #3
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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