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

(1-omega+omega^2)(1-omega^2+omega^4)(1-omega^4+omega^2)…. to 2n Factors = 2^(2n)

If 1, omega , omega^2 are the three cube roots of unity, then (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 is

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

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)

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

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

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