Prove that `(1+w)(1+w^2)(1+w^4)(1+w^8)....... 2n` factors `= 1` ?

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) .

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.

Prove that (1-w+w^2)^5+(1+w-w^2)^5=32

Prove that, (1-w+w^2)^4+(1+w-w^2)^4=-16

(1-w^2+w^4)(1+w^2-w^4)

Prove that (1+w)(1+w^2)(1+w^4)(1+w^8)=1 where w is the imagination cube root of unity.

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

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

If omega is a complex cube roots of unity, then find the value of the (1+ omega)(1+ omega^(2))(1+ omega^(4)) (1+ omega^(8)) … to 2n factors.

If omega is a complex cube root of unity then the value of (1+omega)(1+omega^(2))(1+omega^(4)).......2n terms-