Associates and their Norms - Should be easy

Hello All:

I have two things I'd like to learn 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 $\displaystyle \alpha $ is a set of quadratic integers in $\displaystyle Q[\sqrt{-3}] $ so that $\displaystyle \bar{\alpha} $ and $\displaystyle \alpha $ are associates. Can someone help describe what this set would be like when this occurs?

Thank you! - Samson