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Math Help - Confusing integral

  1. #1
    Junior Member piglet's Avatar
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    Feb 2010
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    Confusing integral

    Show  \int_{C}\frac{1}{z-2}dz = 2\pi.i where  C is a circle of radius  1 centred at  2
    using a parametrization.

    I can show this using Cauchy's Integral formula i.e.
     \int_{C}\frac{f(z)}{z-z0}dz = 2\pi.i.f(z0) but i dont't think this is using a parametrization?

    Any ideas?
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  2. #2
    MHF Contributor chisigma's Avatar
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    Setting s=z-2 the integral becomes...

    \int_{\gamma} \frac{ds}{s} (1)

    ... where \gamma is now the unit circle centered at s=0. Now You set s=e^{i\cdot \omega} and solve the integral in \omega...

    Kind regards

    \chi \sigma
    Last edited by chisigma; April 20th 2010 at 10:46 AM.
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