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Math Help - Possible values for a complex integral

  1. #1
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    Possible values for a complex integral

    Hello,
    How many possible values are there for the following integral-

    \oint_{C}\frac{dz}{(z-z_1)(z-z_2)..(z-z_n)}

    (I'm guessing the answer is not n, but don't see why)

    Should also add that C is a closed contour that does not go through any of the points z_i
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  2. #2
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    Looks like 2^n to me if the poles are simple and residues do not cancel one or more of each other.
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  3. #3
    MHF Contributor Bruno J.'s Avatar
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    Quote Originally Posted by dudyu View Post
    Hello,
    How many possible values are there for the following integral-

    \oint_{C}\frac{dz}{(z-z_1)(z-z_2)..(z-z_n)}

    (I'm guessing the answer is not n, but don't see why)

    Should also add that C is a simple closed contour that does not go through any of the points z_i
    Otherwise there are infinitely many possible values!
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  4. #4
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    Thanks for the replies.
    Well, assuming poles are simple and residues don't cancel each other, I take it there are 2 possible values per point z_i . Why's that?
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  5. #5
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    Just start drawing circles around each combination of poles and include one circle that does not include any and keep in mind I would have gotten this one wrong as per Bruno up there.
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  6. #6
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    Thumbs up

    Got it. Thanks very much!
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