Originally Posted by

**mbmstudent** 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)

Not ony not obvious but even wrong: $\displaystyle |a+b\sqrt{-3}|^2=a^2+3b^2$ , since we're talking here about

the module (=absolute value) of a complex number

, 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!