The value of `(x+w+w^2)(x+w^2+w^4).....`till 2n factors

If w is an imaginary cube root of unity then prove that If w is a complex cube root of unity , find the value of (1+w)(1+w^2)(1+w^4)(1+w^8)..... to n factors.

If w is an imaginary cube root of unity then prove that (1-w+w^2)(1-w^2+w^4)(1-w^4+w^8)....... " to " 2n "factors" =2^(2n) .

The value of (x+omega+omega^(2)) (x +omega^(2)+omega^(4))(x +omega^(4)+omega^(8)) .... till 2n factors

If 1, omega, omega ^(2) are the cube roots of unity, then the value of (x+y) ^(2) + (x omega +y omega ^(2))^(2) + (x omega ^(2)+ y omega )^(2) is equal to-

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=

If omega is a complex cube root of unity, then (1+omega)(1+(omega)^2)(1+(omega)^4)(1+(omega)^8)) ….....upto 2n factors = …....

Show that (a+ omega +omega ^(2))(a+omega ^(2)+omega ^(4))(a+omega ^(4)+omega ^(8))... upto 2n factosrs =(a-1)^(2n) .

Prove the following (1+ omega) (1+ omega^(2)) (1 + omega^(4)) (1 + omega^(8)) ….to 2n factors = 1

If 1,omega,omega^(2) are the cube roots of unity (1+omega)(1+omega^(2))(1+omega^(4))(1+omega^(5))....... to 2n factors