# Proving completeness of subset in $\mathbb{R}^2$

I am struggling with this question about completeness of subsets of sequences.

-Show if the following subset of $\mathbb{R}^2$ with standard metric is complete; if it is, prove; if not, find one Cauchy sequence whose limit is not in the set:

A= $\mathbb{R}^2$ \ $\mathbb{Q} \times \mathbb{Q}$

Any help would be highly appreciated. Thank you very much in advance!

Consider $$x_n=\left(0,\frac{\pi}{n}\right).$$