De moivre’s and euler formulas for matrices of hybrid numbers

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Akbıyık M., Akbıyık S. Y., Karaca E., YILMAZ F.

Axioms, vol.10, no.3, 2021 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.3390/axioms10030213
  • Journal Name: Axioms
  • Journal Indexes: Scopus
  • Keywords: Euler and De Moivre’s formulas, Hybrid numbers, Matrix representation
  • Istanbul Gelisim University Affiliated: Yes


© 2021 by the authors. Licensee MDPI, Basel, Switzerland.It is known that the hybrid numbers are generalizations of complex, hyperbolic and dual numbers. Recently, they have attracted the attention of many scientists. At this paper, we provide the Euler’s and De Moivre’s formulas for the 4 × 4 matrices associated with hybrid numbers by using trigonometric identities. Also, we give the roots of the matrices of hybrid numbers. Moreover, we give some illustrative examples to support the main formulas.