If `omega` be an imaginary cube root of unity, show that ` (a+bomega+comega^2)/(aomega+bomega^2+c) = omega^2`

If omega be an imaginary cube root of unity,show that (1+omega-omega^(2))(1-omega+omega^(2))=4

If omega is a cube root of unity, prove that (a+bomega+comega^2)/(c+aomega+bomega^2)=omega^2

If omega be an imaginary cube root of unity, show that: 1/(1+2omega)+ 1/(2+omega) - 1/(1+omega)=0 .

If |(x^2+x, x-1, x+1), (x, 2x, 3x-1), (4x+1, x-2, x+2)|= px^4 +qx^3+rx^2+sx+t be n identity in x and omega be an imaginary cube root of unity, (a+bomega+comega^2)/(c+aomega+bomega^2)+(a+bomega+comega^2)/(b+comega+aomega^2)= (A) p (B) 2p (C) -2p (D) -p

If omega be an imaginary cube root of unity, show that 1+omega^n+omega^(2n)=0 , for n=2,4 .

If omega is an imaginary cube root of unity, then (1+omega-omega^(2))^(7) equals

If omega is an imaginary cube root of unity, then the value of |(a,b omega^(2),a omega),(b omega,c,b omega^(2)),(c omega^(2),a omega,c)| , is

If omega is an imainary cube root of unity,then show that (1-omega+omega^(2))^(5)+(1+omega-omega^(2))^(5)=32