In this study, we firstly give the basic notations of the generalized complex number plane (-complex plane) . Then, we introduce the one-parameter planar motions in -complex plane such that . These motions correspond the one-parameter motions in affine Cayley-Klein planes . We examine this motion theory with aspects of complex motions as given in . Besides, we discuss the relations between absolute, relative, sliding velocities (accelerations) and pole curves under the motions .