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Math Help - Complex Analysis

  1. #1
    MHF Contributor chiph588@'s Avatar
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    Complex Analysis

    1. If  f is analytic in a closed bounded region  G and  f(z) \neq 0 in  G , show
    that  |f| assumes its minimum value on the boundary of  G .
    Hint: consider  \frac{1}{f} .

    2. Use Problem 1 to prove the Fundamental Theorem of Algebra.
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  2. #2
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    Quote Originally Posted by chiph588@ View Post
    1. If  f is analytic in a closed bounded region  G and  f(z) \neq 0 in  G , show
    that  |f| assumes its minimum value on the boundary of  G .
    Hint: consider  \frac{1}{f} .
    The minimum value of |f| is the maximum value of 1/|f|.
    But 1/|f| assumes it maximum on the boundary by the maximum modulos principle.
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  3. #3
    MHF Contributor chiph588@'s Avatar
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    Thanks!
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