A study on tricomplex polynomials

Year 2026, Issue: Advanced Online Publication, 1 - 9

Djaouida Achour Hacène Belbachir , Abdelkader Bouyakoub

https://doi.org/10.15672/hujms.1663042

Abstract

Tricomplex numbers are a generalization of bicomplex numbers. In this paper, we detail a technique for finding the roots of tricomplex polynomials. We generalized then the process to multicomplex polynomials. We first give an idempotent-representation of tricomplex numbers and reduce the working method to complex polynomials. We give examples to
illustrate the different situations. Finally, for a multicomplex polynomial, we explain a reduction process ending to search roots in the complex field. Combining these give the roots for multicomplex polynomials.

Keywords

Bicomplex numbers , Tricomplex numbers , Multicomplex numbers , Roots of polynomials

References

• 1] M. Bilgin and S. Ersoy. Algebraic properties of bihyperbolic numbers. Adv. Appl. Clifford Algebr. 30, 2020.