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Math Help - Complex variables proof

  1. #1
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    Complex variables proof

    This particular problem is giving me some trouble:

    Suppose that f is an entire function and Re[f(z)] is less than or equal to c for all z. Show that f is constant.
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  2. #2
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    Quote Originally Posted by spoon737 View Post
    This particular problem is giving me some trouble:

    Suppose that f is an entire function and Re[f(z)] is less than or equal to c for all z. Show that f is constant.
    This is a famous famous theorem.
    In fact it gives a super short proof of the fundamental theorem of algebra. Here.

    By the actual theorem is stated and proven. Here.
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