A study on tricomplex polynomials

Year 2026, Volume: 55 Issue: 1 , 176 - 184 , 23.02.2026

Djaouida Achour , Hacène Belbachir , Abdelkader Bouyakoub

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

https://izlik.org/JA45CC85NG

Abstract

Tricomplex numbers are a generalization of bicomplex numbers. In this paper we detail a technic for finding the roots of tricomplex polynomials. We then generalize the process to multicomplex polynomials. We first consider the set of tricomplex numbers as a Bicomplex Module, then we view it as a $\mathbb{C}$-algebra and we reduce the working method to complex polynomials. We give an example to illustrate the different situations. We then calculate the set of all tricomplex $n^{th}$ roots of unity. Finally, for a multicomplex polynomial, we explain a reduction process ending to search roots in the complex field. Combining these gives the roots for multicomplex polynomials.

Keywords

bicomplex numbers , tricomplex numbers , multicomplex numbers , roots of polynomials

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