  A number of recent experiments have suggested the presence of either real or
complex components in the gap symmetry of high-$T_c$ superconductors (HTSC). In
this paper we introduce a novel approach to study the competition of such
complex order parameter mixtures by varying the position of the two-body
attractive potential in a two dimensional extended Hubbard Hamiltonian. We show
that this procedure explain a number of experimental results and on the
theoretical side, it may be related with certain HTSC microscopic models like
the spin fluctuation theory. Following current trends we concentrate on the
study of $d_{x^2-y^2}$ order parameter with a component of the type $d_{xy}$ or
a s-wave like $s_{x^2+y^2}$ and $s_{xy}$ symmetry. We show that the position of
the optimal s-component peak changes with the position parameter $b$ while the
d-component occurs always in the optimally region around hole content $\rho
\approx 0.39$.
