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Math Help - Taylor/ Laurent series expansion question

  1. #1
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    Taylor/ Laurent series expansion question

    Hi, im having much confusion and difficulty in answering this question.Thankyou for any help in advance

    Let f be defined by

    f(z)=\frac{1}{2z^{2}-(1+2i)z+i}

    (a) Find the poles z1 and z2 of f such that \left | z1 \right |< \left | z2 \right |.
    (b) Give the series expansion of f in the following three regions, stating in each case if it is a Taylor or Laurent series.
    i. \left | z \right |< \left | z1 \right |
    ii. \left |z1 \right |< \left | z \right |< \left | z2 \right |
    iii. |z-z1| < |z2-z1|

    Thankyou again.
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    To find the poles, set the denominator equal to  0 .

    i.e. solve  \displaystyle{2z^{2}-(1+2i)z+i=0}
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  3. #3
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    I think this will help you Laurent Series
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