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Math Help - cauchy's integral theorem

  1. #1
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    cauchy's integral theorem

    Im attempting to show that the following is not true by cauchy's integral theorem.

    \int_{C}\frac{\overline{z}}{z^{2} - 5z - 6},dz = 0 where  C is the unit circle (travelled anti-clockwise).

    Resolving  z^{2} - 5z - 6 = 0 i got z = 2 and z = 3 but these singularities lie outside the unit circle...

    I know i need to do something with the  \overline{z} but cant figure out what
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  2. #2
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    Quote Originally Posted by Tekken View Post
    Im attempting to show that the following is not true by cauchy's integral theorem.

    \int_{C}\frac{\overline{z}}{z^{2} - 5z - 6},dz = 0 where  C is the unit circle (travelled anti-clockwise).

    Resolving  z^{2} - 5z - 6 = 0 i got z = 2 and z = 3 but these singularities lie outside the unit circle...

    I know i need to do something with the  \overline{z} but cant figure out what
    Either it is z^2-5z+6 or you did a mistake in computing the roots.

    Anyway, the trick is to notice that, if z\in C, then \overline{z}=\frac{1}{z}, so you can apply Cauchy theorem and there is a pole inside the contour.
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  3. #3
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    ya sorry about that, it should have been  z^{2} - 5z + 6

    Thanks for the help
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