:> > so :> > :> > (x+sqrt(-1)y)(x-sqrt(-1)y) = 0, :> :> > so :> > :> > x+sqrt(-1)y = 0 or x-sqrt(-1)y=0, :>
: It doesn't matter whether or not a and b are complex or not.
: The only possible issue might be made by using something like 3(2)=0 : (mod 6), but we're not talking about a finite ring.
There are plenty of infinite rings in which ab = 0 does not imply a = 0 or b = 0. This comment about finiteness is a non sequitur.
: As for me proving that if ab = 0, a or b equals 0, I'm not interested : in doing that.
: If you need that proof to understand what I'm talking about, oh well.
That is a real shame, since filling in that step is exactly what many posters, including me, asked you to do. If it's so simple that you can safely omit the justification, why not just spare a couple of lines to fill it in?
If you are unable or unwilling to explain your arguments, you will certainly never convince anyone you are right about your more ambitious project. This would be good practice.