# Units in Gauss integers ring

• Nov 1st 2008, 04:32 PM
Units in Gauss integers ring
Find units in a ring constituted by Gauss integers.

So I know that Gauss integers are $a+bi \ \ \ a,b \in \mathbb {Z}$[/tex]

Now, of course $-1, 1, i, -i$ are units, but would $1-i,-1+i$ also be units? And are there anymore?
• Nov 1st 2008, 04:33 PM
ThePerfectHacker
Quote:

So I know that Gauss integers are $a+bi \ \ \ a,b \in \mathbb {Z}$[/tex]
Now, of course $-1, 1, i, -i$ are units, but would $1-i,-1+i$ also be units? And are there anymore?
No. A Gaussian is a unit if and only if $N(\alpha) = 1$. Where $\alpha = a+bi$ and $N(\alpha) = a^2+b^2$.