Re: About Hachel's alternate "complex" numbers

 I did a bit of research to see if the structure that Hachel originally proposed, with these multiplication rules:
(a, b) * (a', b') = (aa' + bb', ab' + a'b)
 had already been studied. Since it is clearly a ring (but not a field, as it has divisors of zero), it seemed likely to me.
 And indeed, it has! This is called the set of split-complex numbers:
https://en.wikipedia.org/wiki/Split-complex_number