On complex hybrid numbers: Algebraic structures, matrix representations, and geometric interpretations

Seçgin F., Ramis İlgüz Ç., GÖK İ.

Kuwait Journal of Science, vol.53, no.1, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 53 Issue: 1
  • Publication Date: 2026
  • Doi Number: 10.1016/j.kjs.2025.100528
  • Journal Name: Kuwait Journal of Science
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
  • Keywords: Complex numbers, Hybrid numbers, Matrix representations, Pauli matrices
  • Ankara University Affiliated: Yes

Abstract

This work introduces complex hybrid numbers, an extension of hybrid numbers, which are defined as Z=z0+z1i+z2ɛ+z3h where zi are complex numbers and ih=−hi=i+ɛ. We investigate their algebraic properties, classify them into ℂ1, ℂ2,D, and P-types, and analyze their matrix representations. Numerical examples illustrate key findings, highlighting both their theoretical structure and potential areas of application. Key findings are demonstrated with numerical examples, emphasizing their structural importance and their uses.