A Study on Dual-Generalized Complex and Hyperbolic-Generalized Complex Numbers

Abstract

This work is intended to introduce the theories of dual-generalized complex and hyperbolic-generalized complex numbers. The algebraic properties of these numbers are taken into consideration. Besides, dual-generalized complex and hyperbolic-generalized complex valued functions are defined and different matrix representations of these numbers are examined. Moreover, a remarkable classification are given for special cases and the set of complex-generalized complex numbers are mentioned.