# Complex partial fraction expansion

I would like to have a tool for partial fraction expansion of polynomial quotient $$\frac{P(z)}{Q(z)},$$ where the order of the polynomial $$P(z)$$ is less than that of $$Q(z)$$.

The output of the function is expected to be the coefficients $$c_{ij}$$ of the expansion: $$\sum_i\sum_{j=1}^{m_i}\frac{c_{ij}}{(z-\zeta_i)^j},$$ where the sum runs over all distinct roots $$\zeta_i$$ (with multiplicity $$m_i$$) of the polynomial $$Q(z)$$.

Is there a built-in function in Mathematica which is suitable for performing the task? For a symbolic computation the list of roots of the polynomial $$Q(z)$$ can be supplied.