Can I simplify $\cos \frac{1234 \pi}{5}$ and $\sin \frac{1234 \pi}{5}$ I have 
$$\cos \frac{1234 \pi}{5} + i \cdot \sin \frac{1234 \pi}{5}$$
I believe I can simplify the $1234$ further, but how?

To complement mrf, we can say that $cos(\frac{1234 \pi}{5})=cos(\frac{4 \pi}{5}$).  Because there are the periodic identities which stays that:
$\sin( \theta+ 2 \pi n)= \sin \theta $
$\cos( \theta+ 2 \pi n)= \cos \theta \qquad n \in \mathbb{Z}$
This happens because the period of sine and cosine funtions is $2 \pi$.
