Theoretical and numerical considerations on the polar (exponential) form of octonions and elements of higher-order Cayley-Dickson algebras

The article is devoted to the issue of the polar form of octonions. This is a~continuation of the works initiated by Hahn and Snopek in their articles from 2011. The results presented in the article show errors made in previous considerations and suggest the possibility of their improvement. The presented numerical method gives promising results, which as a result of further work can give analytical formulas for angles in the polar representation.