An efficient method for solving equations in generalized quaternion and\n octonion algebras

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