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Math Help - Quick Residue theorem question

  1. #1
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    Quick Residue theorem question

    I just have a quick question on a problem in the text book,

    Determine the singular points of:

    1/(z^3+i)

    Am i right in assuming there are only 2 singular point, z=(-i)^1/3 and z= i.

    And they are simple poles?

    No answer in the book

    Thanks for your help.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Re: Quick Residue theorem question

    Quote Originally Posted by olski1 View Post
    I just have a quick question on a problem in the text book,

    Determine the singular points of:

    1/(z^3+i)

    Am i right in assuming there are only 2 singular point, z=(-i)^1/3 and z= i.

    And they are simple poles?

    No answer in the book

    Thanks for your help.
    Well, I think you should know that there are three 3-roots of unity. And then, z^3=i\Leftrightarrow (iz)^3=1 should tell you how many solutions there are.
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