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Math Help - [SOLVED] Complex Analysis: integrals & residue thereom

  1. #1
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    [SOLVED] Complex Analysis: integrals & residue thereom

    Hi there, I'm asked to evaluate the following integral counterclockwise

    \int\limits_{|z| = 2}^{ }({1 - cosz})/({z^2 - z}) dz

    The residue theorem doesn't work, as taking singularities at z = 0 and z = 1, I get 0 as the result for the residue when z = 0. I don't know what else to do, any advice would be appreciated.
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  2. #2
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    Quote Originally Posted by pineapple89 View Post
    Hi there, I'm asked to evaluate the following integral counterclockwise

    \int\limits_{|z| = 2}^{ }({1 - cosz})/({z^2 - z}) dz

    The residue theorem doesn't work, as taking singularities at z = 0 and z = 1, I get 0 as the result for the residue when z = 0. I don't know what else to do, any advice would be appreciated.
    try letting  cosz = \frac{1}{2}(z+\frac{1}{z}) and then tidy up  f(z)
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