(v) If `1, w, w^2` are cube roots of unity, show that, `(1+w)(1+w^2)(1+w^4)(1+w^8) =1`

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

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

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

If, 1, omega, omega^(2) are cube roots of unity, show that (p + qomega + r omega^(2))/(r + p omega + q omega^(2))= omega^(2)

If w is a complex cube root of unity. Show that |[1,w, w^2],[w, w^2, 1],[w^2, 1,w]|=0 .

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

If omega is a cube root of unity, then 1+omega = …..

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