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Math Help - Complex analysis

  1. #1
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    Complex analysis

    Hey guys.
    I have this question, I took it from a test.
    I need to check if there is an analytic function F(z) in this area (in the pic) that has this derivative (in the pic).

    http://img256.imageshack.us/img256/7826/25453238.jpg

    Well, the derivative is analytic in this area, right?
    If the derivative is analytic, shouldn't F(z) be analytic and even more important, can it be that easy ?
    I'm not sure about the answer, I could really use some help.

    Thanks a lot.
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  2. #2
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    Opalg's Avatar
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    The integral of \frac z{z^2+4} is \tfrac12\ln(z^2+4), and this function cannot be defined globally on the set \mathbb{C}\setminus\{\pm2i\} (logarithm functions can usually only be defined on some kind of cut plane).
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