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Math Help - Argument Principle

  1. #1
    MHF Contributor chiph588@'s Avatar
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    Argument Principle

    In Complex Analysis the argument principle says  \int_c \frac{f'(z)}{f(z)}dz = 2\pi i(N-P) = i\Delta_c \arg(f(z)) .

    I'm having a tough time understanding why the second equality is true. I feel like I'm probably missing something little. Any thoughts?

    Thanks
    -Chip
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    By the second equality, you mean : 2\pi i(N-P) = i\Delta_c \arg(f(z))?

    The equality is proven by showing that both of these terms are equal to the integral on the left, by evaluating the integral once using the residue theorem, and once by considering it as the integral of d \log f.
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