  We solve a new chiral Random Two-Matrix Theory by means of biorthogonal
polynomials for any matrix size $N$. By deriving the relevant kernels we find
explicit formulas for all $(n,k)$-point spectral (mixed or unmixed) correlation
functions. In the microscopic limit we find the corresponding scaling
functions, and thus derive all spectral correlators in this limit as well. We
extend these results to the ordinary (non-chiral) ensembles, and also there
provide explicit solutions for any finite size $N$, and in the microscopic
scaling limit. Our results give the general analytical expressions for the
microscopic correlation functions of the Dirac operator eigenvalues in theories
with imaginary baryon and isospin chemical potential, and can be used to
extract the tree-level pion decay constant from lattice gauge theory
configurations. We find exact agreement with previous computations based on the
low-energy effective field theory in the two special cases where comparisons
are possible.
