(1+2 omega+omega^(2))^(3n)-(1+omega+2 omega^(2))^(3n)=

The value of (1+omega^(2)+2 omega)^(3n)-(1+omega+2 omega^(2))^(3n) is

The value of (1+omega^(2)+2 omega)^(3 n)-(1+omega+2 omega^(2))^(3 n)=

If 1,omega,omega^(2) are the roots of unity then (1-omega+omega^(2))^(3)+(1+omega-omega^(2))^3=

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.

The value of the expression 1.(2- omega)(2- omega^(2)) + 2.(3-omega) (3-omega^(2)) + …+ (n-1)(n- omega)(n- omega^(2)) , where omega is an imaginary cube root of unity is

Suppose omega ne 1 is cube root of unity. If 1(2-omega) (2-omega^(2)) + 2(3 - omega) (3 - omega^(2)) + ….+ (n-1)(n-omega) (n-omega^(2)) = 33 , then n is equal to ____________

If omega be an imaginary cube root or unity, prove that (1- omega+ omega^(2)) (1-omega^(2)+ omega^(4)) (1- omega^(4)+ omega ^(8))..."to" 2 n th factor =2^(2n)