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Math Help - Question on Rouche Theorem -2

  1. #1
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    Question on Rouche Theorem -2

    f(z) is analytic inside and on a closed path C. f(z) is real for all z on C.
    Prove f(z) is constant.

    Stuck for quite a while on this. Any help please?
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  2. #2
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    Text says that this is a direct application of Rouche Theorem. Rouche's theorem is about zero's - not sure how to link that with f(z) being constant.

    I was trying something on the lines that f'(z) is zero at every point. Thus f(z) is constant.

    Will request any pointers here please. Thanks
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