In the context of electrical engineering, j is often used to denote the imaginary unit, that is, something such that j^2 = -1; in other words it's the same as what is usually called 'i'.
But, in the context of the split-complex numbers, j is something such that j^2 = 1, and i suppose it is writen as 'j' to distinguish it from 'i'.
So, the 'j' used here is different from the 'j' used in electrical engineering.
For example, if j were the square root of -1, as in electrical engineering, then (8j - 5)^2 would equal -39 - 80j: 64j^2 - 80j + 25 = -64 -80j + 25 = -39 - 80j; but here, in the split-complex numbers, (8j - 5)^2 = 64j^2 -80j + 25 = 64 - 80j + 25 = 89 - 80j.
But, in the context of the split-complex numbers, j is something such that j^2 = 1, and i suppose it is writen as 'j' to distinguish it from 'i'.
So, the 'j' used here is different from the 'j' used in electrical engineering.
( https://en.wikipedia.org/wiki/Split-complex_number )
For example, if j were the square root of -1, as in electrical engineering, then (8j - 5)^2 would equal -39 - 80j: 64j^2 - 80j + 25 = -64 -80j + 25 = -39 - 80j; but here, in the split-complex numbers, (8j - 5)^2 = 64j^2 -80j + 25 = 64 - 80j + 25 = 89 - 80j.