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Math Help - Complex Integration

  1. #1
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    Complex Integration

    No contour is given for the following problem.It has a singularity at z=0, therefore Not path independent.How would you go about doing the integration? Integrate and Evaluate at the end points?


    Integral of [((2*z)-6)/(z(z-2))] from (-1-i) to (1+i)
    Last edited by heatly; April 1st 2014 at 05:13 PM.
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  2. #2
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    Re: Complex Integration

    Quote Originally Posted by heatly View Post
    No contour is given for the following problem.It has a singularity at z=0, therefore Not path independent.How would you go about doing the integration? Integrate and Evaluate at the end points?


    Integral of [((2*z)-6)/(z(z-2))] from (-1-i) to (1+i)
    You need to break the integral into 3 contours to avoid the singularity at 0.

    the first is a line from $\large (-1-\imath) \to \epsilon e^{-\imath \frac{3\pi}{4}}$

    the second is a semicircle of radius $\epsilon$ from $\large \epsilon e^{-\imath \frac {3 \pi}{4}} \to \epsilon e^{\imath \frac {\pi}{4}}$

    the third is a line from $\large \epsilon e^{\imath \frac {\pi}{4}} \to (1+\imath)$

    you should be able to formulate these contours and integrate. Use partial fractions to break up the integrand into recognizable pieces. Take the limit as $\epsilon \to 0$
    Thanks from heatly
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    Re: Complex Integration

    Thanks very much for that.
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