Explore BrainMass

Explore BrainMass

    Complex Polynomials, Roots and Residue Theory

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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).

    © BrainMass Inc. brainmass.com March 4, 2021, 7:00 pm ad1c9bdddf
    https://brainmass.com/math/number-theory/complex-polynomials-roots-residue-theory-75739

    Attachments

    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using BrainMass.

    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.

    $2.49

    ADVERTISEMENT