<firstname.lastname@example.org> wrote in message news://email@example.com...
> Let's say that I'm in some other ring besides integers. All the > results I've given are still true. That is, > > (x+sqrt(-1)y)(x-sqrt(-1)y) = x^2 + y^2, and if x^2 + y^2 = 0, then > > (x+sqrt(-1)y)(x-sqrt(-1)y) = 0. > > You've all been insisting that I have to know what ring x and y are in > to prove whether or not this means that > > (x+sqrt(-1)y) = 0 *or* (x-sqrt(-1)y) = 0.
1. What is x and y?
2. What is sqrt(-1) exactly?
3. How are the operations (+,*) defined?
4. In what ring (if any) are (x + sqrt(-1)y) and (x - sqrt(-1)) in?