# Complex Polynomials, Roots and Residue Theory

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Let P(z) and Q(z) be complex polynomials of degree m and n respectively, such that Q(z) has distinct roots z1...zn. Assume that n >= m+2 . Prove that P(z1)/Q'(z1) +...+ P(zn)/Q'(zn) (hint: evaluate ∫c P(z)/Q(z) dz for a suitable curve C).

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Question

Let P(z) and Q(z) be complex polynomials of degree m and n respectively, such that Q(z) has distinct roots . Assume that . Prove that (hint: evaluate for a suitable curve C).

Answer

Firstly let us recall the important result about Residue Theory:

Where the sum is over the poles inside the ...

#### Solution Summary

Complex Polynomials, Roots and Residue Theory are investigated.

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