Complex Residues. Let P(s)/Q(s) be a rational function
Chapter 7, Problem 42E(choose chapter or problem)
Complex Residues. Let P(s)/Q(s) be a rational function with deg P < deg Q and suppose (s-?)2 + ?2 is a nonrepeated quadratic factor of Q. (That is, are complex conjugate zeros of Q.) Prove that the portion of the partial fraction expansion of P(s)/Q(s) corresponding to (s-?)2+?2 is where the complex residue ?B+i?A is given by the formula (Thus we can determine B and A by taking the real and imaginary parts of the limit and dividing them by ?.)
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