Dual complex Pell quaternions

TL;DR

This paper introduces dual complex Pell numbers and quaternions, exploring their algebraic properties and deriving identities like Binet's and Cassini's, expanding the mathematical framework of Pell-related structures.

Contribution

It defines dual complex Pell numbers and quaternions and investigates their algebraic properties and identities, which is a novel extension in the study of Pell-related algebraic systems.

Findings

Derived algebraic properties of dual complex Pell numbers and quaternions

Established identities such as Honsberger, Binet's, Cassini's, and Catalan's for these quaternions

Connected dual complex Pell structures with classical Pell number identities

Abstract

In this paper, dual complex Pell numbers and quaternions are defined. Also, some algebraic properties of dual-complex Pell numbers and quaternions which are connected with dual complex numbers and Pell numbers are investigated. Furthermore, the Honsberger identity, Binet's formula, Cassini's identity, Catalan's identity for these quaternions are given.