Question

If 1,w,w^2 are cube roots of unity then prove that (1+w) (1+w)^2 (1+w)^4 (1+w)^8....... 2n = 1

Answer 1

If 1,W,W2 is cube roots of unity then…
1+W+W2=0 and W3=1
Now,
1+W2=-W
So,
1+W2-W=-2W. eqn1
Now,
1+W+W2=0
1+W=-W2
So,
1-W2+W=-2W2. eqn2
Now
eqn1×eqn2=4W3
Therefore W3=1
4 is answer

Answer 2

Hope it helps u....