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How many branches does a complex function have?

  1. Dec 19, 2012 #1
    1. The problem statement, all variables and given/known data
    How many branches does the function
    [tex] f(z) = \sqrt{z(1-z)} [/tex] have on the set [tex] \Omega = \mathbb{C} \backslash [0,1] [/tex]

    2. Relevant equations

    3. The attempt at a solution

    Not really sure how to go about it at all. Our lecturer didn't say too much about branches but still expects everyone to be able to handle them, the only example he's given us is a branch of log(z), which isn't too bad as it just involves restricting the argument.

    Any help at all would be appreciated.
  2. jcsd
  3. Dec 19, 2012 #2


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    2017 Award

    Staff: Mentor

    Hint: How many complex roots does a complex number have?
  4. Dec 20, 2012 #3
    Alright, so [tex] z(z-1) [/tex] will have two square roots, so will the answer just be two?
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