यदि इकाइ के घनमूल `omega` हो तो `(1+ omega- omega^(2))^(7)`=

(1- omega + omega^(2))^(7) + (1 + omega - omega^(2))^(7) =

If 1 , omega , omega^(2) are the cube roots of unity prove that (1 - omega + omega^(2))^(6) + ( 1 - omega ^(2) + omega)^(6) = 128 = (1 - omega + omega^(2))^(7) + ( 1 + omega - omega^(2))^(7)

If 1 , omega + omega^(2) are the cube roots of unity prove that (i) (1 - omega + omega^(2))^(6) + (1 - omega^(2) + omega)^(6) = 128 = ( 1 - omega + omega^(2))^(7) + ( 1 + omega - omega^(2))^(7) (ii) ( a+ b) ( aomega+b omega^(2))( a omega^(2) + b omega) = a^(3) + b^(3) (iii) x^(2) + 4x + 7 = 0 " where " x = omega - omega^(2) - 2 .

(1-omega +omega^2)(1+omega-omega^2)=4

(1+omega-omega^(2))(1-omega+omega^(2))

(1-omega+omega^(2))^(7)+(1+omega-omega^(2))^(7)

(1-omega+omega^(2))(1+omega-omega^(2))=4

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

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