Advances in Applied Clifford Algebras

, Volume 25, Issue 2, pp 337–350 | Cite as

An Efficient Method for Solving Equations in Generalized Quaternion and Octonion Algebras

  • Cristina Flaut
  • Vitalii Shpakivskyi


Quaternions often appear in wide areas of applied science and engineering such as wireless communications systems, mechanics, etc. It is known that are two types of non-isomorphic generalized quaternion algebras, namely: the algebra of quaternions and the algebra of coquaternions. In this paper, we present the formulae to pass from a basis in the generalized quaternion algebras to a basis in the division quaternions algebra or to a basis in the coquaternions algebra and vice versa. The same result was obtained for the generalized octonion algebra. Moreover, we emphasize the applications of these results to the algebraic equations and De Moivre’s formula in generalized quaternion algebras and in generalized octonion division algebras.


Generalized quaternion algebras de Moivre’s formula 


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© Springer Basel 2014

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceOvidius UniversityConstantaRomania
  2. 2.Department of Complex Analysis and Potential TheoryInstitute of Mathematics of the National Academy of Sciences of UkraineKiev-4Ukraine

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