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Homework Help: Branch points [Complex Analysis]

  1. Jan 25, 2015 #1
    1. The problem statement, all variables and given/known data
    Hi, I'm stuck with this question:
    How many branches (solutions) and branch points does the function
    f(z) = (z2 +1 +i)1=4 have? Give an example of a branch of the multi-
    valued function f that is continuous in the cut-plane, for some choice
    of branch cut(s). Now by choosing different branch cut(s), provide a
    different example.

    2. Relevant equations
    f(z) = (z2 +1 +i)1=4

    3. The attempt at a solution
    So I've done the first part, by setting f(z) = 0 then solving for two solutions of z to be sqrt(-1-i) and z= -sqrt(-1-i), but I'm not sure how to proceed onto the next part of the question.
  2. jcsd
  3. Jan 25, 2015 #2


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    Science Advisor
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    Gold Member

    What does that expression mean? It looks like maybe z2+1+i, but what is the final 1 doing?
  4. Jan 25, 2015 #3
    Woops sorry! The function z is meant to say (z^2+1+i)^1/4
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