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Math Help - Question regarding branch cuts of a function

  1. #1
    Junior Member
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    Question regarding branch cuts of a function

    I am struggling with these question about branch cuts.

    The function f(z) is given by:

    f(z) = [(z-1)^p][(z+1)^q]

    where p and q are real constants.

    The branch of this function is chosen such that

    0 <= arg(z +- 1) < 2 π

    Show that, if and only if p + q = integer, a branch cut is not need on the section (1, ∞) of the real axis.

    Deduce where the cut is in this case.
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  2. #2
    Super Member
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    Aug 2008
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    See this thread:

    S.O.S. Mathematics CyberBoard :: View topic - Branches of (z-1)^a (z+1)^b

    In that case, I think the branch cut is then [-1,1].
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