In this paper, we investigate Mobius groups theory in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero-divisors. We shall generalize classical Jorgensen' inequality to bicomplex analysis and obtain an analogue of Jorgensen type inequality for discrete non-elementary Mobius groups of bicomplex setting generated by two elements.

The author thanks the referee for the valuable suggestions which greatly improve the paper and are helpful for the further research of the related topics. The research has been supported by the National Nature Science Foundation of China ( No.11771266.)