See:

https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/Though personally I prefer:

a+ib+j(c+id)+k(e+if+j(g+ih))

or a+jb+k(c+jd) where a to d are complex

or a+kb where a and b are of the form x+jy where x and y are complex

4D x+jy gives the equivalent results for complex x,y as x+iy does for real x,y

8D x+ky similarly

I prefer these simply because the 4D form x+jy with x and y complex is commutative whereas quaternions aren't and the fact that standard polynomial fractals at least for the 4D form don't give the whipped-cream produced using quaternions