Complex numbers: $ (\sqrt{3}+ i)^{30} $ to 'a + ib' form How do I rewrite this to 'a + ib' form? The power of 30 is troubling me. 
$ (\sqrt{3}+ i)^{30} $

Hint. Since $|\sqrt{3}+i|=2$, we have that
$$(\sqrt{3}+ i)^{30}=2^{30}\left(\frac{\sqrt{3}}{2}+ \frac{i}{2}\right)^{30}=2^{30}\left(\cos(\pi/6)+ i\sin(\pi/6)\right)^{30}.$$
Then use De Moivre's Formula.
