cube roots of unity are Z1=-1+root3i / 2 Z2=-1-root3i / 2 Z3=1
Z1,Z2 are called w,w^2
so there are therr roots of unity 1,w,w^2
1+w+w^2=0
w^3=1
like this you can also calculate 4th,5th,.........,nth root,too.
for nth root of unity 1^n=1,e^i(2pi/n),e^i(4pi/n)...........,e^i[2(n-1)pi/n] n=1,2,......
here sum of all root=0
product of root is = ( -1)^n+1