The Real Matrices forms of the Bicomplex Numbers and Homothetic Exponential motions

Abstract

In this paper, a bicomplex number is described in four- dimensional space and its a variety of algebraic properties is presented. In addition, Pauli-spin matrix elements corresponding to base the real matrices forms of the bicomplex numbers are obtained and its the algebraic properties are given. Like i and j in two different spaces are defined terms of Euler's formula. In the last section velocities become higher order by giving an exponential homothetic motion for the bicomplex numbers. And then, Due to the way in which the matter is presented, the paper gives some formula and facts about exponential homothetic motions which are not generally known.