  The dynamics of the second order rational difference equation
$\displaystyle{z_{n+1}=\frac{\alpha + \alpha z_{n}+\beta z_{n-1}}{1+z_{n}}}$
with complex parameters $\alpha$, $\beta$ and arbitrary complex initial
conditions is investigated. The same difference equation is well studied with
positive real parameters and initial values and one of the main results on
trichotomy of parameters is revisited in the complex set-up and the similar
result is found to be true. In addition, the chaotic solutions of the equation
is fetched out in the complex set-up which was absent in the real scenario.
