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 the cube roots of unity, then the value of (1+omega)(1+omega^(2))(1+omega^(4))(1+omega^(8)) is

2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation "x^(2) - 3mx + 2m^(2) = 0 " has both roots positive, where " alpha gt 0 and beta gt 0. If omega, omega^(2) are the cube roots of unity, then (1+omega) (1+omega^(2))(1+omega^(3)) (1+ omega + omega ^(2)) is equal to

If omega is a cube root of unity,then (1+omega)^(3)-(1+omega^(2))^(3)=

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