Evaluate :
`w^2 + w^3 + w^4`

Evaluate : ( 1 + w ) ( 1 - w^2 + w ) + w^2

Evaluate : ( 1 - 3w + w^2 ) ( 1 + w - 3w^2 )

cos ((2 pi) / (7)) + i sin ((2 pi) / (7)) and alpha = w + w ^ (2) + w ^ (4) and beta = w ^ (3) + w ^ (5) + w ^ (6)

Find the value of w^4+w^6+w^8 , if w is a complex cube root of unity.

Evaluate: | (1, 1, 1), (1, omega^2, omega), (1, omega, omega^2)| (where omega is an imaginary cube root unity).

Find the value of w : -2/3 = 6/w

If w is the imaginary cube root of unity evaluate |(1,w,w^2),(w,w^2,1),(w^2,1,w)|

Evaluate: (i) omega (ii) omega^(2) (iii) omega^(3)