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Math Help - Finding poles

  1. #1
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    Finding poles

    Find all poles of f(z)=\frac{\sin^2 z}{z^3+8i} and state the order of the poles.

    Do I need to do a full Laurent expansion of this? Or is there an easier way?

    EDIT: I guess it seems to have a pole of order 1 at 2i?
    Last edited by scorpion007; May 16th 2010 at 07:55 PM.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by scorpion007 View Post
    Find all poles of f(z)=\frac{\sin^2 z}{z^3+8i} and state the order of the poles.

    Do I need to do a full Laurent expansion of this? Or is there an easier way?

    EDIT: I guess it seems to have a pole of order 1 at 2i?
    I would agree with your edited answer.
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  3. #3
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    I worked on this a bit more and found 3 unique poles by solving z^3=-8i and DeMoivre's theorem. Thanks anyhow.
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