Showing that the Klein 4-group $V_4$ and the cyclic group $Z_4$ are not isomorphic

Question

How do you show that the Klein $4$-group $V_4$ and $Z_4$ are not isomorphic? I want to use the following fact:

If $f\colon G \to H$ is an isomorphism, then $|f(x)| = |x|$ for all $x \in G.$

Answer 1

The group $Z_4$ is cyclic and it's generator has order four. If you did have an isomorphism $f\colon Z_4 \to V_4$, is there an element of order four in $V_4$ for that generator to map to?