Quadratic Fields and Norms
I had a few more questions about Quadratic Fields and Norms from the example section of my reading. (By the way, I am very appreciative of all of the help I've received so far!) Here are my questions:
Note: Q[x] denotes the Quadratic Field of x, N(y) denotes the Norm of y.
1. There exists integers 'd' for which the field Q[Sqrt(d)] has elements 'a' with negative norm N(a), assuming that d is not a perfect square. Does anyone know what these 'd' is and how to prove this? This seems really general...
2. Examining Q[Sqrt(-1)], an equation can be written relating N(a) to |a| where | | means the natural absolute value defined for complex numbers. What is this equation and for which Q[Sqrt(d)] would this formula be correct? (Undefined previously posted a relation in another problem, please see
Thank you everyone! I really appreciate the help!