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Math Help - sum, zeros, poles

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    sum, zeros, poles

    Let f(z)=\frac{p(z)}{q(z)}, where p(z) and q(z) are polynomials. Prove that the sum of multiplicities of all zeroes minus the sum of orders of all poles, including zeroes or poles at \infty, equals zero.


    I am not sure how to prove this. I was thinking to use the argument principle somehow. However, could not figure out how. I need some hints on how this one. Thanks.
    Last edited by xboxlive89128; February 19th 2010 at 03:36 PM.
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