`(2+omega+omega^2)^3+(1+omega-omega^2)^8-(1-3omega+omega^2)^4=1`

Prove the following (1- omega + omega^(2)) (1 + omega- omega^(2)) (1 - omega- omega^(2))= 8

If omega is complex cube root of unity (1-omega+ omega^2) (1-omega^2+omega^4)(1-omega^4+omega^8)(1-omega^8+omega^16)

If omega be a complex cube root of unity, then the number (1-omega-omega^2)^3+(omega-1-omega^2)^3+(omega^2-omega-1)^3 is: a. Divisible by 3 but not by 8 b. Divisible by 8 but not by 3 c. Divisible by both 3 & 8 d. none of these

If omega is a complex cube root of unity then (1-omega+omega^2)(1-omega^2+omega^4)(1-omega^4+omega^8)(1-omega^8+omega^16)

Prove that (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))(1-omega^(8)+omega^(16)).... to 2^(n) factors = 2^(2n) .

If omega(ne1) is a cube root of unity, then (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …upto 2n is factors, is

Prove the following (1- omega + omega^(2)) (1- omega^(2) + omega^(4)) (1- omega^(4) + omega^(8)) …. to 2n factors = 2^(2n) where , ω is the cube root of unity.

If 1, omega, omega^(2) are three cube roots of unity, prove that (1+ omega- omega^(2))^(3)= (1- omega + omega^(2))^(3)= -8

If omega is cube roots of unity, prove that {[(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)]=[(0),(0),(0)]

If omega is cube roots of unity, prove that {[(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)]=[(0),(0),(0)]