Introduction to Hybrid Numbers


ÖZDEMİR M.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, vol.28, no.1, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.1007/s00006-018-0833-3
  • Journal Name: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Complex numbers, Hyperbolic numbers, Dual numbers, Non-comutative rings, De Moivre formulas, ROTATION MATRIX, COMPLEX NUMBER, DUAL NUMBERS, REPRESENTATIONS
  • Akdeniz University Affiliated: Yes

Abstract

In this study, we define a new non-commutative number system called hybrid numbers. This number system can be accepted as a generalization of the complex (i(2) = -1), hyperbolic (h(2) = 1) and dual number (epsilon(2) = 0) systems. A hybrid number is a number created with any combination of the complex, hyperbolic and dual numbers satisfying the relation ih = -hi = i + epsilon. Because these numbers are a composition of dual, complex and hyperbolic numbers, we think that it would be better to call them hybrid numbers instead of the generalized complex numbers. In this paper, we give some algebraic and geometric properties of this number set with some classifications. In addition, we examined the roots of a hybrid number according to its type and character.