If `w` is cube root of unity then prove that, `(3+3 omega+5 omega^(2))^(6)-(2+6 omega+2 omega^(2))^(3)=0`

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

If 1, omega, omega^(2) are three cube roots of unity, prove that (3+ 5omega + 3omega^(2))^(6) = (3 + 5omega^(2) + 3omega)^(6)= 64

If omega and omega^(2) are cube roots of unity, prove that (2- omega + 2omega^(2)) (2 + 2omega- omega^(2))= 9

Given that 1, omega, omega^(2) are cube roots of unity. Show that (1- omega + omega^(2))^(5) + (1 + omega - omega^(2))^(5)= 32

If omega is a cube root of unity, then omega^(3) = ……

If 1, omega and omega^(2) are the cube roots of unity, prove that (a+b omega+c omega^(2))/(c+a omega+b omega^(2))=omega^(2)

If 1, omega, omega^(2) are the three cube roots of unity, then simplify: (3 + 5omega + 3omega^(2))^(2) (1 + 2omega + omega^(2))

If omega, omega^2 be imaginary cube root of unity then (3 +3 omega + 5 omega^2) ^6 - (2 + 6omega + 2 omega^2)^3 is equal to

If 1, omega, omega^(2) are cube roots of unity, prove that (x + y)^(2) + (x omega + y omega^(2))^(2) + (x omega^(2) + y omega)^(2)= 6xy