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We are given two polynomials p, q with deg(q)>1+deg(p). Show that the sum of the residue at all poles of the rational function p/q is 0.

How do I go about solving this?

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Hint: Let $\gamma_R$ be a circle of radius $R$ around 0 such that all zeros of $q$ lie inside $\gamma_R$. What can you say for $\int_{\gamma_R} \frac pq \, dz$ for $R \to \infty$? How can you connect this with the residue sum?

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    as $R \to \infty$, p/q goes to zero?2014-04-22