  The dynamics of the delay logistic equation with complex parameters and
arbitrary complex initial conditions is investigated. The analysis of the local
stability of this difference equation has been carried out. We further exhibit
several interesting characteristics of the solutions of this equation, using
computations, which does not arise when we consider the same equation with
positive real parameters and initial conditions. Some of the interesting
observations led us to pose some open problems and conjectures regarding
chaotic and higher order periodic solutions and global asymptotic convergence
of the delay logistic equation. It is our hope that these observations of this
complex difference equation would certainly be an interesting addition to the
present art of research in rational difference equations in understanding the
behaviour in the complex domain.
