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Complex Logarithms

  1. Jan 21, 2010 #1
    1. The problem statement, all variables and given/known data


    tan-1z = (1/2i)ln[(1+iz)/(1-iz)]

    then find

    tan-1[(2sqrt(3) - 3i)/7]

    3. The attempt at a solution

    I haven't gotten very far, but this is what I have so far:

    tan-1[(2sqrt(3) - 3i)/7]

    = (1/2i)ln[(i2sqrt(3) + 10)/(i2sqrt(3) + 4)]

    Where do you go from there? I'm not completely familiar with the rules of complex logarithms. Can you split it into real and imaginary parts?
  2. jcsd
  3. Jan 21, 2010 #2


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    Science Advisor
    Homework Helper

    You should check what you already have. I think you've already got a sign wrong. But you want write the expression inside the log in the form a+bi with a and b real, so you can find it's magnitude and angle. You know how to do that with a ratio using complex conjugates, right?
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