Prove that $\forall z \in \Bbb C, \exists x \in \Bbb Z[j], |z-x|\leq \frac{\sqrt3}{2}$

Question

Need help proving that $\forall z \in \Bbb C, \exists x \in \Bbb Z[j], |z-x|\leq \frac{\sqrt3}{2}$ \ where $\Bbb Z[j]=\{a+jb / a,b \in \Bbb Z\}$ and $j=e^{\frac{i2\pi}{3}}$.
I thought of using the fact that $(1,j)$ is a basis of $\Bbb C$ and then trying the floor of the coordinates of $z$ but no luck.