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Homework Help: Complex Analysis - Contour Intergral

  1. Oct 15, 2008 #1
    1. The problem statement, all variables and given/known data

    The problem is to integrate:

    [tex]\oint_{C}\frac{dz}{z^{2}-1}[/tex]

    C is a C.C.W circle |z| = 2.

    2. Relevant equations



    3. The attempt at a solution

    I used the Cauchy integral formula:

    [tex]\oint_{C}\frac{f(z)}{(z-z_{0})^{n+1}}dz = \frac{2 \pi i}{n!}f^{n}(z_{0})[/tex]

    Which gives an answer of [tex]2 \pi i[/tex] since there is a singularity inside of the contour C...

    Does this look right?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 15, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    That's not right at all. z^2-1 is not the same as (z-1)^2. And even if the problem were dz/(z-1)^2 the integral of that around |z|=2 would be zero (since f(z) in your formula is 1). Use z^2-1=(z-1)(z+1) and then look up the residue theorem. Or write 1/((z-1)(z+1))=A/(z-1)+B/(z+1) (figure out A and B) and then you can use the Cauchy integral formula on each part.
     
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