Then, on the second part of it, they say:

Let F be a field. Let's assume there's an a(that belongs to)F, so that a^2+1=0 . Prove that FxF isn't a field.

I can understand that it's like asking me to prove that a,b on Z=a+bi has to be that (a,b(belong to)R) on a field, because in this question it's asked to prove that it's impossible that there would be a field with (a,b) so that (a,b) can be imaginary.

Now, in order to prove that a group is NOT a field, it's enough to show that it has a,b(belong to)F so that a,b(are not equal to zero), and a*b=0.

I just couldn't find any way to prove that ^...

Would any of you mind to help me?

Thank you very much