Get the Numerator and Denominator of the Laplace Transform S-Domain Transfer Functions

Hello,

I have troubles to understand how to convert the vectors of real and complex poles and residues of a rational function model into real numerators and denominators of Laplace Transform S-domain.

Concerning the demo "Modeling a High-Speed Backplane" I have one questions to section "Get the Numerator and Denominator of the Laplace Transform S-Domain Transfer Functions"

Where do I get informations why the numerator and denomiator looks like this if complex poles occur? rat_num{k} = [2*real_c, -2*(real_a*real_c+imag_a*imag_c)]; rat_den{k} = [1, -2*real_a, real_a^2+imag_a^2];

Has somebody an idea? Is there some literature where I can look this up?

Thanks, Matthias