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Integrating complex functions

  1. Nov 13, 2016 #1
    1. The problem statement, all variables and given/known data
    Evaluate the following line integrals in the complex plane by direct integration.
    upload_2016-11-13_21-56-9.png
    2. Relevant equations
    Z= x+i y = Cos(θ) +i Sin(θ) = e^i*θ
    3. The attempt at a solution
    I'm not sure how to evaluated this by hand. I tried using Z= x+i y = Cos(θ) +i Sin(θ), and evaluating the integral at dθ. However, I'm not sure how to change the bounds. It seems to me that point A starts at 2pi, and then point B is at 2pi + i *(infinity). what exactly does that mean?
     

    Attached Files:

  2. jcsd
  3. Nov 13, 2016 #2

    ehild

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    You overcomplicate the problem. Do the integral with respect to z, as if it was a common real number. Then substitute the limits for z, using that the upper limit means z=x+iy=2pi + iy, y-->infinity.
     
  4. Nov 13, 2016 #3
    I see. That is what I wanted to do at first. However, I was taken back by the complex part of the upper bound. I see now that I really over complicated that problem.

    Thank you!
     

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