`(1+omega-omega^2)^3 - (1-omega+omega^2)^3 = `

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

If omega be a complex cube root of unity,then the number (1-omega-omega^(2))^(3)+(omega-1-omega^(2))^(3)+(omega^(2)-omega-1)^(3) is: a.Divisible by 3 but not by 8 b.Divisible by 8 but not by 3 c.Divisible by both 3 & 8 d.none of these

(2 + omega + omega ^ (2)) ^ (3) + (1 + omega-omega ^ (2)) ^ (3) = (1-3 omega + omega ^ (2)) ^ (4) = 1

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

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

The value of (1+omega^(2)+2 omega)^(3n)-(1+omega+2 omega^(2))^(3n) is

Which of the following is a non singular matrix? (A) [(1,a,b+c),(1,b,c+a),(1,c,a+b)] (B) [(1,omega, omega^2),(omega, omega^2,1),(omega^2,1,omega)] where omega is non real and omega^2=1 (C) [(1^2,2^2,3^2),(2^2,3^2,4^2),(3^2,4^2,5^2)] (D) [(0,2,-3),(-2,0,5),(3,-5,0)]