AM  Vol.12 No.2 , February 2021
Powers of Octonions
Abstract: As it is known, Binomial expansion, De Moivre’s formula, and Euler’s formula are suitable methods for computing the powers of a complex number, but to compute the powers of an octonion number in easy way, we need to derive suitable formulas from these methods. In this paper, we present a novel way to compute the powers of an octonion number using formulas derived from the binomial expansion.
Cite this paper: Ahmed, W. (2021) Powers of Octonions. Applied Mathematics, 12, 75-84. doi: 10.4236/am.2021.122006.

[1]   Dray, T. and Manogue, C.A. (2015) The Geometry of Octonions. World Scientific.

[2]   Baez, J. (2002) The Octonions. Bulletin of the American Mathematical Society (New Series), 39, 145-205.

[3]   Conway, J.H. and Smith, D.A. (2003) On Quaternions and Octonions. Their Geometry, Arithmetic, and Symmetry. A K Peters Ltd., Boca Raton.

[4]   Graves, R.P. (1882) Life of Sir William Rowan Hamilton. Hodges Figgis, Dublin.

[5]   Cayley, A. (1845) On Jacobi’s Elliptic Functions, in Reply to the Rev. Brice Bornwin; and on Quaternions. Philosophical Magazine Series, 26, 208-211.

[6]   Tian, Y. (2000) Matrix Representations of Octonions and Their Applications. Advances in Applied Clifford Algebras, 10, 61.

[7]   Bektaş, Ö. and Yüce, S. (2019) De Moivre’s and Euler’s Formulas for the Matrices of Octonions. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 89, 113-127.