  Herein we propose a complex form of a genuine Bernstein-Durrmeyer type
operators depending on a non-negative real parameter $\alpha.$ We present the
quantitative upper bound, Voronovskaja type result and exact order of
approximation for these operators and for their derivatives attached to
analytic functions on compact disks. These results validate the extension of
approximation properties of complex genuine $\alpha-$Bernstein-Durrmeyer type
operators from real intervals to compact disks in the complex plane.
