Let $(X, ||\cdot||)$ be a complete normed space. Let $||\cdot||$ be a norm on $X$, and assume that there are constants $c_{1}$, $c_{2} \in (0,\infty)$ such that:
$c_{1}||x-y||\le||x-y||_{0}\le c_{2}||x-y||$
for all $x,y\in X.$ Show that $(X,||\cdot||_{0})$ complete.
To be honest I have absolutely no idea where to start.