  The correlation functions of the multi-arc complex matrix model are shown to
be universal for any finite number of arcs. The universality classes are
characterized by the support of the eigenvalue density and are conjectured to
fall into the same classes as the ones recently found for the hermitian model.
This is explicitly shown to be true for the case of two arcs, apart from the
known result for one arc. The basic tool is the iterative solution of the loop
equation for the complex matrix model with multiple arcs, which provides all
multi-loop correlators up to an arbitrary genus. Explicit results for genus one
are given for any number of arcs. The two-arc solution is investigated in
detail, including the double-scaling limit. In addition universal expressions
for the string susceptibility are given for both the complex and hermitian
model.
