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Math Help - Complex Variables

  1. #1
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    Complex Variables

    Can anyone help me with this pls?

    How can you prove that the integral of f(z) around the contour z= 1 is 0

    where f(z) is Log(z+5)

    Thx
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  2. #2
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    I know Log(z) is ln r + i (theta). But i dont know how that applies to this situation.

    Also, do I solve it as a normal integral or use the Cauchy Goursat theorem to prove that its integral is zero?
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  3. #3
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    Quote Originally Posted by stillsoulsearching View Post
    Can anyone help me with this pls?

    How can you prove that the integral of f(z) around the contour z= 1 is 0

    where f(z) is Log(z+5)

    Thx
    Because \log (z+5) is analytic on \mathbb{C} - (\infty,-5]. This is a simply connected domain and Cauchy's theorem tells us that the integral over a (rectifiable) curve of an analytic function on a simply connected domain is zero.
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