1) Find for which integers d the field $\displaystyle \mathbf{Q}\left(\sqrt{d}\right)$ has elements $\displaystyle \alpha$ with negative norm $\displaystyle N(\alpha)$. Assume d is not a perfect square.

2) Consider $\displaystyle \mathbf{Q}\left(\sqrt{-1}\right)$. Write an equation relating $\displaystyle N(\alpha)$ to $\displaystyle |\alpha|$ (the natural absolute value defined for complex numbers). For which $\displaystyle \mathbf{Q}\left(\sqrt{d}\right)$ is this formula correct?

How do you approach these questions?

Thanks.