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Complex Analysis: countour integral

  1. Jan 7, 2012 #1
    1. The problem statement, all variables and given/known data

    Compute the contour integral I around the following curve $\Gamma$:

    $ I = \int_\Gamma \dfraq{dz}{z^2 +1} $

    see picture:
    http://dl.dropbox.com/u/26643017/Screen%20Shot%202012-01-07%20at%2010.39.58.png [Broken]

    2. Relevant equations

    3. The attempt at a solution

    $\Gamma$ is an open curve, but even if you close it with a line from A to B an the real axis, you may not use cauchy's theorem and calculate it with the residue theorem, because it is not a "smooth curve"...
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jan 7, 2012 #2


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    The curve doesn't have to be "smooth" to apply Cauchy's theorem. It only has to be rectifiable. Piecewise smooth is plenty good enough.
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