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Branch points and branch cuts

  1. Nov 3, 2008 #1
    Hey guys,

    I need to find the branch cut of the function f(z) = Log[z^2 +9] where the negative real axis has been removed from the domain of the log function. Now this is the bit that confuses me, is this saying that we must ensure that no negative real components enter the argument of the log function or is it saying theyre not part of the domain dont worry about them?

    Anyway, i factor it out and you get f(z) = log(z+3i)+log(z-3i). My understanding is the branch cut is the line segment(s) on which the function is discontinuous, so are we just saying that the imaginary part of z must be >3i or <-3i ? I'm a bit confoosed =(

    Cheers
    -G
     
  2. jcsd
  3. Nov 4, 2008 #2

    benorin

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    Homework Helper

    The angle the branch cut makes with the negative real axis is not always 0, is it plum?
     
  4. Nov 4, 2008 #3

    Avodyne

    User Avatar
    Science Advisor

    No
    Yes. So, this means that the branch cut of log(z) lies on the negative real axis. And that means that the branch cut of log(z^2+9) lies ... where?
     
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