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Homework Help: Branch Cut

  1. Mar 27, 2010 #1
    1. The problem statement, all variables and given/known data Branch cut for cos(sqrt(z)).



    2. Relevant equations



    3. The attempt at a solution Apparently there is no need for a branch cut for this function, but I am not sure why - I heard it has something to do with cos being an even function. Any clarification would be appreciated.
     
  2. jcsd
  3. Mar 27, 2010 #2

    Hurkyl

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    I'm sure you've done an exercise like writing down all of the values of a multivalued function like sqrt(z) in terms of ordinary functions. (e.g. in terms of the principal branch Sqrt(z))

    That seems like an obvious place to start to me.
     
  4. Mar 27, 2010 #3
    You mean write z as r*exp(i(t+2*k*pi)), so sqrt(z) = (r^1/2)*exp(it/2) or (r^1/2)*exp(i(t/2+pi)? = -(r^1/2)*exp(it/2) ?
     
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