`(1-w+w^2)^5+(1+w-w^2)^5=32`

If 1, w, w^(2) are three cube roots of unity, then (1 - w+ w^(2)) (1 + w-w^(2)) is _______

If w is an imaginary cube root of unity then prove that (1-w)(1-w^2)(1-w^4)(1-w^5)=9

If w is a complex cube root of unity, then show that (1-w) (1- w ^(2)) (1 - w ^(4)) ( 1 - w ^(5)) = 9

If omega is an imaginary cube root of unity, then show that (1-omega+omega^2)^5+(1+omega-omega^2)^5 =32

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

If 1,omega,omega^2 are the cube roots of unity then prove the following i) (1-omega+omega^2) + (1+omega-omega^2)^5=32 ii) (x+y+z)(x+yomega+zomega^2)(x+yomega^2+zomega)=x^3+y^3+z^3-3xyz

(1-omega+(omega)^2)^5+(1+omega-(omega)^2)^5 =