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Is f(z)+i arg(z) an analytic function?

  1. May 15, 2015 #1
    Solve.jpg
    Is this function analytic or not? Please explain
     
  2. jcsd
  3. May 15, 2015 #2

    Svein

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    Well, it's the definition of log(z).
     
  4. May 15, 2015 #3
    so how to split ln (z) and arg (z) for determining analyticity?
     
  5. May 15, 2015 #4

    Svein

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    log(z) is analytic in any simply connected domain that does not include 0.

    By the way, the expression ln|z| is the real logarithm.
     
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