De Moivre’s and Euler Formulas for Matrices of Hybrid Numbers

Abstract

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.

On the Generalized Gaussian Fibonacci Numbers and Horadam Hybrid Numbers: A Unified Approach

“…Considering this extension, new results have been published in the literature. The reader is referred to [18][19][20][21][22][23][24] and the references therein.…”

Generalized k-Order Fibonacci Hybrid Quaternions

“…They gave some number sequences for special values of 𝑘. In [5], the authors obtained the Euler's and De Moivre's formulas for the 4 × 4 matrix representation of hybrid numbers. Moreover, they gave the roots of the matrix representation of hybrid numbers and some results.…”

On Powers and Roots of Split Octonions

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