Completeness of Normed spaces. I want to prove the following proposition
If $(X,||\cdot||)$ and $(X,||\cdot||')$ are homeomorphic, then $(X,||\cdot||)$ is complete if and only if $(X,||\cdot||')$ is complete.
So, I only know the definition of homeomorphic, and can't figure out how only with that I can prove that proposition. Can someone help me to prove this please?
Thanks a lot in advance :) 

Take a Cauchy sequence in $(X,||\cdot||)$ and show that is also a Cauchy sequence in $(X,||\cdot||')$.
This proves the assertion since convergence is a topological property which is preserved by homeomorphisms.
