Q. Show Conjugate Complex Poles?

It is possible that some of the poles of Equation are complex. Since the coefficients ak in Equation are real, complex poles occur in complex conjugate pairs and will always be even in number. Let us consider a pair of complex poles for which case Equation may be written as

The procedure for finding K₁ and K₂ is the same as outlined earlier for unrepeated linear factors or simple poles. Thus we have

It can be shown that K₁ and K₂ are conjugates of each other. The terms in the time function, L^-1 [F(s)], due to the complex poles of F (s), are then found easily.