`(1-omega+omega^2)^7+(1+omega-omega^2)^7 = `

If 1, omega, omega^2 be three roots of 1, show that: (1-omega+omega^2)^2+(1+omega-omega^2)^2=-4

(1-omega+omega^(2))(1+omega-omega^(2))=4

Prove that (1-omega-omega^(2))(1-omega+omega^(2))(1+omega-omega^(2))=8

If 1,omega,omega^(2) are the roots of unity then (1-omega+omega^(2))^(3)+(1+omega-omega^(2))^3=

If 1,omega,omega^(2) are the cube roots of units then find (1-omega+omega^(2))^(4)+(1+omega-omega^(2))^(8)

If 1, omega, omega^2 be the cube roots of unity, then the value of (1 - omega + omega^2)^(5) + (1 + omega - omega^2)^5 is :