If `1, omega, omega^2` be three roots of 1, show that: `(1+omega)^3-(1+omega^2)^3=0`

If 1, omega, omega^2 be three roots of 1, show that: (3+omega+3omega^2)^6=64

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

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

If 1, omega, omega^2 be the three cube roots of 1, then show that: (1+omega)(1+omega^2)(1+omega^4)(1+omega^8)=1

If 1, omega, omega^(2) are three cube roots of unity, prove that (1+ omega- omega^(2))^(3)= (1- omega + omega^(2))^(3)= -8

If 1, omega, omega^(2) are three cube roots of unity, prove that (1- omega- omega^(2))^(6)= 64

If 1, omega, omega^(2) are three cube roots of unity, show that (a + omega b+ omega^(2)c) (a + omega^(2)b+ omega c)= a^(2) + b^(2) + c^(2)- ab- bc - ca

If 1, omega, omega^(2) are three cube roots of unity, prove that (1- omega) (1- omega^(2))= 3

If 1, omega, omega^(2) are three cube roots of unity, prove that (1 + omega - omega^(2)) (1- omega + omega^(2))=4

If 1, omega, omega^(2) are the cube roots of unity, prove that (1 + omega)^(3)-(1 + omega^(2))^(3)=0