Intuitive understanding of Lemma of Jordan

Question

Can somebody give me an intuitive understanding of the Lemma of Jordan, which is:

$$\lim \limits_{R\rightarrow \infty} \int_{\gamma} \exp(i \omega z)\,\rm dz=0 $$

if:

$$\lim \limits_{z\rightarrow \infty} f(z) =0, \omega>0$$