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

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 (1-w)(1-w^2)(1-w^4)(1-w^5)=9

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

If i=sqrt(-1),w is non real cube root of unity then ((1+i)^(2n)-(1-i)^(2n))/((1+w^(4)-w^(2))(1-w^(4)+w^(2)))

If w be an imaginary cube root of unity, prove that (1-w+w^2)^2+(1+w-w^2)^2=-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 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.

If1,w,w^(2) be three cube roots of 1, show that: (1+w-w^(2))(1-w+w^(2))=4 and (3+w+3w^(2))^(6)=64

if 1,w,w^(2) we be the three cube roots of 1, then show that : (1+w)(1+w^(2))(1+w^(4))(1+w^(5))=1

Show that : ( 1 + w - w^2 ) ( w + w^2 - 1 ) ( w^2 + 1 - w ) = -8