  We employ a ghost model of interacting dark energy to obtain the equation of
state \omega for ghost energy density in an FRW universe in complex
quintessence theory. We reconstruct the potential and study the dynamics of the
scalar field that describes complex quintessence cosmology. We perform
\omega-\omega' analysis and stability analysis for both non-interacting and
interacting cases and find that the same basic conclusion as for the real
model, where \omega' = d\omega/dlna. Taking account of the effect of the
complex part and assuming the real part of the quintessence field to be a
"slow-rolling" field, we conclude that the non-interacting model cannot
describe the real universe since this will lead to fractional energy density
\Omega_D > 1, where \Omega_D can be defined as the ratio of \rho_D to
\rho_{cr}. However, for the interacting case, if we take present \Omega_D =
0.73, then we can determine that b^2 = 0.0849, where b^2 is the interaction
coupling parameter between matter and dark energy. In the real quintessence
model, \Omega_D and b^2 are independent parameters, whereas in the complex
quintessence model, we conclude that there is a relationship between these two
parameters.
