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Homework Help: A complex integral

  1. Oct 5, 2007 #1
    1. The problem statement, all variables and given/known data
    Let [tex] \gamma_{r} [/tex] be the circle centered at 2i with a radius r. Compute:

    [tex]\oint \frac{f(z)}{z^{2}+1}dz [/tex]

    2. Relevant equations

    [tex]2 \pi i f(w)=\oint \frac{f(z)}{z-w}dz[/tex]

    Cauchy's integral formula... maybe?

    3. The attempt at a solution

    I can see how to find solutions for two separate cases:


    I have no idea how to find a general formula for this... nor am I sure what to do when [tex]\gamma[/tex] passes thru a singularity...

    any help on how to get started would be MUCH appreciated... thanks in advance
  2. jcsd
  3. Oct 5, 2007 #2


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    Science Advisor
    Homework Helper

    If the curve passes through the singularity then it's really only defined in the principle value sense. I wouldn't worry about that case. But you are doing it right. You have to split the answer into cases, not write on big formula.
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