Partial Fraction Expansion over Complex Numbers with Mathematica

(*Function Definition*)
FactorC[p_, x_] :=
Times @@ Cases[Roots[p == 0, x, Cubics -> False], u_ == v_ -> x - v]

PartialFractionsC[p_,
x_] := (Apart[Numerator[#1]/FactorC[Denominator[#1], x], x] &)[
Together[p]]

(*Example: Transfer function to be decomposed*)
R := (A s)/(s^2 + \[Omega]^2)

PartialFractionsC[R, s]

A/(2 (s - I \[Omega])) + A/(2 (s + I \[Omega]))