Could anyone help me find this limit $$\limsup_{|z|\to\infty}\frac{\log|e^{-iz}|}{|z|}$$
where $z=x+iy, x,y\in \mathbb R$.
I guess we need to use that $e^{-iz}=\cos z- i\sin z$, then $$\limsup_{|z|\to\infty}\frac{\log|e^{-iz}|}{|z|}=\limsup_{|z|\to\infty}\frac{\log|\cos z- i\sin z|}{|z|}$$
but what next?