inequality involving complex exponential Is it true that 
$$|e^{ix}-e^{iy}|\leq |x-y|$$ for $x,y\in\mathbb{R}$? I can't figure it out. I tried looking at the series for exponential but it did not help.
Could someone offer a hint? 

Hints: $e^{ix} -e^{iy}= e^{ix}(1 -e^{i(y-x)})$, and $|e^{ix}|=1$. Let $\theta=x-y$.
