If `w` is a complex cube root of unity. Show that `|1w w^2w w^2 1w^2 1w|=0` .

If w is a complex cube root of unity.Show that |1ww^(2)ww^(2)1w^(2)1w|=0

If w is a complex cube root of unity. Show that |[1,w, w^2],[w, w^2, 1],[w^2, 1,w]|=0 .

If w is a complex cube root of unity, show that ([[1,w,w^2],[w,w^2,1],[w^2,1,w]]+[[w,w^2,1],[w^2,1,w],[w,w^2,1]])*[[1],[w],[w^2]]=[[0],[0],[0]]

If w is a complex cube root of unity, show that (1 + w - w ^(2))^(6) = 64

If w is a complex cube root of unity, then show that (1-w) (1- w ^(2)) (1 - w ^(4)) ( 1 - w ^(5)) = 9

If w is a complex cube root of unity, then show that (1 - w + w ^(2)) ^( 5) + (1 + w - w ^(2)) ^( 5) = 32

If w is a complex cube root of unity, prove that (1 - w + w ^(2)) ^(6)+(1 + w - w ^(2)) ^(6) = 128