We investigate the Conjugacy Classification in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero-divisors. In this paper, we first classify bi-complex Möbius transformation in terms of fixed points in BC. Then we have a discussion of the iterates of a bicomplex Möbius transformation and study the attractive and repulsive fixed points in bicomplex setting.
Mathematics Subject Classification (2010). Primary 30G35; Secondary 32A30.