The Multicomplex Numbers and Their Properties on Some Elementary Functions

Md. Nasiruzzaman, M. Mursaleen

Abstract

In this paper, we introduce the some algebraic properties in idempotent form of bicomplex space and multicomplex space, which is the generalization of the field of complex numbers.We describe how to define elementary functions such as polynomials, exponential functions,trigonometric functions, Taylor series for multicomplex holomorphic functions, algebra of eigenvaluescorresponding to an eigenvector on multicomplex space. Finally, our goal are to show that the functionstheory on multicomplex space and multicomplex polynomial are in some sense a better generalizationthan the bicomplex space and bicomplex Polynomial.