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} $

"By hand":
$$(\sqrt3+i)^2=3-1+i2\sqrt3=2(1+i\sqrt3)$$
$$(\sqrt3+i)^3=2(1+i\sqrt3)(\sqrt3+i)=8i.$$
Then
$$(\sqrt3+i)^{30}=(8i)^{10}=(-64)^5=-1073741824.$$
