Complex Numbers in Exponential form

Hey guys, got some questions which I need help in:

1) Express w = (10-2.(sq. root 3)i)/(1-3(sq.root 3)i) in the exponential form and hence or otherwise find the smallest +ve integer n such that w^n is a real number.

I expressed in exponential form and got w = 2e^i(\pi /3) but I got no idea how to do the 2nd part...

Another similar question which I need help in is this:

2)Given that z = (sq. root 3) + i, express z in the exponential form. Hence, find the real value of k such that z^5 + kz* = 0

Again, I only know how to express in exponential form... z = 2e^i(\pi /6) (Thinking)

Please help! Thanks in advance!