Danubius International Conferences, 16th International Conference on European Integration - Realities and Perspectives
Some Solutions of the Equation X2+Ax+B=0 with Elements of Type Quaternion Fibonacci
Last modified: 2021-05-12
Abstract
In this paper we present some solutions of the equation x2+ax+b=0, where a, b in H(1,1), are two elements of type quaternion Fibonacci. Quaternions are non-commutative hypercomplex numbers obtained by extending the set of complex numbers in a manner similar to that which led from real to complex numbers. These numbers were introduced by the Irish mathematician Sir William Rowan Hamilton in 1843 and applied in three-dimensional space. His work influenced the further development of quantum mechanics. Although they have been replaced in applications by vectors, quaternions are still used in both theoretical and applied mathematics, especially for calculations involving three-dimensional rotations. Algebra H (ß1, ß2) is not always a division algebra and, sometimes, it is difficult to find examples of invertible elements.
Acknowledgments: This work is supported by the project “ANTREPRENORDOC”, in the framework of Human Resources Development Operational Programme 2014-2020, financed from the European Social Fund under the contract number 36355/23.05.2019 HRD OP /380/6/13 – SMIS Code: 123847.
