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Math Help - Complex Variables: Contour Integral

  1. #1
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    Complex Variables: Contour Integral

    Let C=C1UC2 where C1 and C2 are respectively the smaller arcs of the circles |z-i|=1 and |z-1|=1 joining the points z1=0+0i and z2=1+i

    By using the definition of a contour integral evaluate

    Complex Variables: Contour Integral-capture.png
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  2. #2
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    Re: Complex Variables: Contour Integral

    This is a closed path isn't it? Unless I misunderstood the question and it isn't, the integral will be 0 by Cauchy's integral theorem.
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    Re: Complex Variables: Contour Integral

    Yes but I'm not sure how to parametrize the curves in order to solve it by integrating directly
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    Re: Complex Variables: Contour Integral

    First of all draw a picture to see what C looks like, it is crucial when doing this kind of integrals.
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