Euclidean domain

Question

Verify that $R=\{a+b\frac{1+i\sqrt{7}}{2}|a,b\in \mathbb{Z}\}$ is Euclidean Domain. Here I think it is a ED. I tried to take norm function $N(a+b\frac{1+i\sqrt{7}}{2})=(a+\frac{b}{2})^2+\frac74b^2.$ But still I am confused how to use Division Algorithm to check the existence of $q$ and $r$ such that $a=bq+r$. I would appreciate for your help.