Relatively Prime Quadratic Integers

Hello All,

I was working on problems involving relatively prime quadratic integers. Here is the one that has me miffed.

Assume that $\displaystyle 32 = \alpha \beta$ for $\displaystyle \alpha , \beta$ relatively prime quadratic integers in $\displaystyle Q[i]$. From here, it can be shown that $\displaystyle \alpha = \epsilon * \gamma^2$ for some unit $\displaystyle \epsilon$ and some quadratic integer $\displaystyle \gamma$ in $\displaystyle Q[i]$.

Could someone help explain how that statement is true?