Electromagnetic energy conservation with complex octonions

Octonions are the eight dimensional hypercomplex numbers that form a noncommutative and nonassociative division algebra. In this study, a general framework for the real, complex octonions and their algebra are provided by using the Cayley-Dickson multiplication rule between the octonionic basis elements. Maxwell s equations without sources are shown in Gauss units in dimensionless form. The local energy conservation equation, which has been previously defined in a complexified quaternionic form, is similarly rearranged for isotropic media by using the complex octonions. As a result, the terms of density and flow of electromagnetic energy are attained