Let R = {$\displaystyle m+n*\sqrt{2}$ |$\displaystyle m,n \in Z$}

Q: Show that $\displaystyle 1+2\sqrt{2}$ has infinite order in $\displaystyle R^x$

From previous part of the Problem:

$\displaystyle m+n*\sqrt{2}$ is a unit in R if and only if $\displaystyle m^2-2n^2= \pm{1}$

I'm a little confused by this since according to the above theorem $\displaystyle 1+2\sqrt{2}$ is not a unit

What am I missing? Is it actually a unit?