Find all elements a+b(-3)^0.5 in Z[-3^0.5] such that |a+b(-3)^0.5|^2=1

Hi,

I have the following problem:

"Find all elements $\displaystyle a+b(-3)^{0.5}$ in $\displaystyle Z[-3^{0.5}]$ such that $\displaystyle |a+b(-3)^{0.5}|^2=1$"

And I think I have the answer, but I don't know if it is right since it says "elements" and not "element."

Well, I know that $\displaystyle |a+b(-3)^{0.5}|^2=a+b(-3)^{0.5}$ (obvious), and that if $\displaystyle a+b(-3)^{0.5}$ is a unit, then $\displaystyle |a+b(-3)^{0.5}|^2=1$... is that correct?

Thanks!