  The pairing interaction is one of the most important contribution of the
residual interaction and then, it is of major importance for the study of
many-body systems. One can get solutions of the pairing Hamiltonian throught
the Bardeen-Cooper-Schieffer (BCS) or the Lipkin-Nogami (LN) approximations
but, the pairing Hamiltonian admit exact solution worked out by Richardson.
Nuclei far away from the stability line have important correlations with the
continuum part of the energy spectrum, due that the Fermi level is very close
to the contiuum thershold. The correlations with the continuum can be included
in the many-body description through the complex energy states, called Gamow
states. In this work we compare the approximates and exact solutions of the
pairing Hamiltonian in real and complex-energy representations. In the
application of this formulation to the symmetric Lipkin model, we found that
the LN solution is in a good agreement with the exact one; besides, the
extension of the BCS solution to the complex energy plane gives solution even
for strength below the critical one, which is purely imaginary.
