u/Alarmed_Ad1946

In other words, does a number like this make sense?
i^2 = -1
j^2 = 1 (j ≠ 1, j ≠ -1)
ε^2 = 0 (ε ≠ 0)

z = a+bi+cj+dε+e(ij)+f(iε)+g(jε)+h(ijε)

I tried making a multiplication table, and I didnt notice any contradictions so far, but when I tried to google I didnt find anything about them, so they´re maybe not useful or dont make sense, I dunno