i. w^k=cis2pik/9
solutions of z^9=1:
1 is a solution, and other solutions are spaced equally around unit circle.
Therefore, z=cis2pik/9 are the solutions where k = 0,1,2...8.
and therefore z=w^k. (Not sure if this is a proof...)
ii. R.T.P w^8 +w^7... +1=0
0=z^9 -1 =(z^3-1)(z^6+z^3+1)=(z-1)(z^2...