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Math Help - prove that

  1. #1
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    prove that

    if f is analytic in a domain D and f is real valued on D then f is constant on D :
    proof :
    im z =0 on D
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  2. #2
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    Quote Originally Posted by flower3 View Post
    if f is analytic in a domain D and f is real valued on D then f is constant on D :
    proof :
    im z =0 on D
    It follows immediatly from the fact that every non constant analytic function f on a domain D is an open mapping. Assume f not to be constant and you will get an easy contradiction using this fact.
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