Quick Quadratic Field Problem

Hello All,

I forgot to throw this into the QFields and Norms thread, and I'm not sure if I should exhume it considering I already gave out thanks and all.

Anyways, my book says that an element exists in Q[Sqrt(-1)] that is not a quadratic integer but its norm in Q[Sqrt(-1)] is an integer.

I tried taking it back to fundamentals like had previously been suggested, but here is what I get.

x=Sqrt(-1)

(x^2)=-1

(x^2)-1=0

I also know that if x = Sqrt(-1), then X = i, so then I have have (i^2)-1=0 from my last statement. I don't see how that helps me prove what I need to, but its a start.

All help is appreciated!