Prove that `(1-omega-omega^(2))(1-omega+omega^(2))(1+omega-omega^(2))=8`

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) .

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

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

Without expanding at any stage, prove that |{:(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega):}| = 0

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):}] where omega is the cube root of unit.

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))

If 1,omega,omega^(2) are cube roots of unity then (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) is equal to

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