Relatively Prime Quadratic Integers

Hello Math Help Forum,

I saw the following problem on another forum but the responses were all over the place and I was hoping if someone could give some clarity. The problem states:

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

Can someone explain how this is shown?