Existence of a metric on $\Bbb Q$ which is complete and equivalent to the usual metric.

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Does there exist a metric $d$ on $\Bbb Q$ which is equivalent to the usual metric on $\Bbb Q$ such that $(\Bbb Q,d)$ is complete?

I have a confusion regarding that. Because I know that equivalence of metrics doesn't preserve completeness for arbitrary metric spaces. Please help me in this regard.

Thank you very much.