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I have two things I'd like to learn more about:

1. I was noticing that the norms of +-1+-i (which are associates) are the same. The same goes for +-(1-2i). Is there a general reason explaining why any two integers which are associates have the same norm?

2. Assume that 'a' is a set of quadratic integers in Q[Sqrt(-3)] so that [tex]\bar{a}[/tex] and 'a' are associates. Can someone help describe what this set would be like when this occurs?