`(1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))(1-omega^(8)+omega^(16))`

If omega is an imaginary cube root of unity, show that (x+omega+ omega^(2))(x-omega^(2)-omega^(4))(x+omega^(4)+omega^(8))(x-omega^(8)-omega^(16)).."to" 2n factors =(x^(2)-1)^(n)

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

(1-omega)(1-omega^(2))(1-omega^(4))(1-omega^(5))(1-omega^(7))(1-omega^(8))

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

(1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …….. to 2n factors

(1 - omega + omega^(2)) ( 1 - omega^(2) + omega^(4)) ( 1- omega^(4) + omega^(8)) to 2n factors =

Arrange the following values in descending order A)(1+omega)(1+omega^2)(1+omega^4)(1+omega^8) B) (1-omega+omega^2)^7+(1+omega-omega^2)^7 C)(1-omega)(1-omega^2)(1-omega^4)(1-omega^8) D) (1-omega+omega^2)(1-omega^2+omega^4)

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)

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.

(1 - omega) (1 - omega^(2)) (1 - omega^(4)) (1 - omega^(5)) (1 - omega^(7)) (1 - omega^(8)) =