Alternate Representation for Complex Poles

Complex poles can be combined to yield a quadratic term in the partial fraction expansion. The representation may best be illustrated by considering one real pole and two complex conjugate poles. Let us then consider

Since Equation must hold for all values of s, the coefficients of various powers of s on both sides of the equality must be equal. These equations of equality are then solved to determine K₂ and K₃.

Even if many pairs of complex conjugate poles occur, this procedure may be used, remembering that the partial fraction for each complex conjugate pair will be of the form discussed.