DUAL-COMPLEX NUMBERS AND THEIR HOLOMORPHIC FUNCTIONS

Farid Messelmi (1)

1 Lama - Lama

The purpose of this paper is to contribute to development a general theory of dual-complex numbers. We start by define the notion of dual-complex and their algebraic properties. In addition, we develop a simple mathematical method based on matrices, simplifying manipulation of dual-complex numbers. Inspired from complex analysis, we generalize the concept of holomorphicity to dual-complex functions. Moreover, a general representation of holomorphic dual-complex functions has been obtained. Finally and as concrete examples, some usual complex functions have been generalized to the algebra of dual-complex numbers.

Domaines: Mathématiques [math]

Farid Messelmi. DUAL-COMPLEX NUMBERS AND THEIR HOLOMORPHIC FUNCTIONS. 2015. ⟨hal-01114178⟩