Suppose $\displaystyle \rho \in \mathbb{Z}[i] $ and that $\displaystyle \lambda(\rho) = r $ is prime in $\displaystyle \mathbb{Z} $. Show that $\displaystyle \rho $ is prime in $\displaystyle \mathbb{Z}[i] $.

I think the easiest way is to use the contrapositive, but I'm not sure.