If `omega = cis (2pi)/(3)`, then number of distinct roots of `|(z+1,omega,omega^(2)),(omega,z + omega^(2),1),(omega^(2),1,z+omega)|` = 0.

Let omega be the complex number cos((2pi)/3)+isin((2pi)/3) . Then the number of distinct complex cos numbers z satisfying Delta=|(z+1,omega,omega^2),(omega,z+omega^2,1),(omega^2,1,z+omega)|=0 is

If is a cubeth root of unity root of : (1-omega+omega^(2))^(4)+(1+omega-omega^(2))^(4) is :

Prove that the value of determinant |{:(1,,omega,,omega^(2)),(omega ,,omega^(2),,1),( omega^(2),, 1,,omega):}|=0 where omega is complex cube root of unity .

If omega is the cube root of unity, then then value of (1 - omega) (1 - omega^(2))(1 - omega^(4))(1 - omega^(8)) is

If omega is a cube root of unity, then find the value of the following: (1+omega-omega^2)(1-omega+omega^2)

If omega is the cube root of unity then Assertion : (1-omega+omega^(2))^(6)+(1+omega-omega^(2))^(6)=128 Reason : 1+omega+omega^(2)=0

If 1, omega omega^(2) are the cube roots of unity then show that (1 + 5omega^(2) + omega^(4)) ( 1 + 5omega + omega^(2)) ( 5 + omega + omega^(5)) = 64.

If omega is a complex cube root of unity, then (a+b omega+c omega^(2))/(c+a omega+b omega^(2))+(c+a omega+b omega^(2))/(a +b omega+c omega^(2))+(b+c omega+a omega^(2))/(b+c omega+a omega^(5))=