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Homework Help: F depends only on |z| then f must be constant?

  1. Mar 22, 2012 #1
    1. The problem statement, all variables and given/known data
    I am stuck on an exercise in the complex analysis course. The problem is:
    "Show that the only analytic functions f that depends on only |z| must be the constant functions."

    2. Relevant equations

    3. The attempt at a solution
    I am not sure if I undertand the question, is it f(z)=|z|, or maybe f(z)=g(|z|)?
  2. jcsd
  3. Mar 22, 2012 #2


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    Staff Emeritus
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    Gold Member

    It's the lattet. Note this is equivalent to saying that f is constant on each circle of radius r
  4. Mar 22, 2012 #3
    Thanks a lot!
    I'll try to solve this now, I'll be back if I get stuck. ;)
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