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

Seçgin F., Ramis İlgüz Ç., GÖK İ.

Kuwait Journal of Science, cilt.53, sa.1, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 53 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1016/j.kjs.2025.100528
  • Dergi Adı: Kuwait Journal of Science
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: Complex numbers, Hybrid numbers, Matrix representations, Pauli matrices
  • Ankara Üniversitesi Adresli: Evet

Özet

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.