As a continuation to my last thread, there are other examples that I struggled with.
1. There exists a defining equation for the golden ratio: (1+Sqrt(5))/2 , and its norm in Q[Sqrt(5)] can also be found.
Can anyone help me find this equation and the norm? I tried to think of it like normalizing vectors and using conjugates, but I don't think that its getting me anywhere.
2. Assuming a and b are elements of Q[Sqrt(d)],, it can be shown that N(ab)=N(a)N(b) and N(a/b)=N(a)/N(b).
How can this be shown? Should a exist in Q, how can we show that N(a)=(a^2) ?
Any and all help is appreciated!