" G) "w+(1)/(w)=-(a)-

If 1, w, w^(2) are three cube roots of unity, then (1 - w+ w^(2)) (1 + w-w^(2)) is _______

Show that : ( 1 + w - w^2 ) ( w + w^2 - 1 ) ( w^2 + 1 - w ) = -8

if 1 , omega ,omega^2 ,............. omega^(n-1) are nth roots of unity , then (1-omega) (1-omega^2).......(1-omega^(n-1)) equal to

(1)/(2+omega)+(1)/(1+2 omega)=(1)/(1+omega)

(1)/(2+omega)+(1)/(1+2 omega)=(1)/(1+omega)

If w is a complex cube root of unity, then the value of the determinant Delta = [(1,w,w^(2)),(w,w^(2),1),(w^(2),1,w)] , is

Let G= {1, w, w^(2)} where w is a complex cube root of unity. Then find the inverse of w^(2) . Under usual multiplication.

{[(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega)] + [(omega,omega^(2),1),(omega^(2),1,omega),(omega,omega^(2),1)]} [(1),(omega),(omega^(2))]