`(1-omega+omega^2)^5 + (1+omega-omega^2)^5`

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

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

If 1,omega,omega^(2) are the cube roots of units then find (1-omega+omega^(2))^(4)+(1+omega-omega^(2))^(8)

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

If omega is an imaginary cube root of unity then prove that If omega is the cube root of unity, Find the value of (1+5omega^2+omega^4)(1+5omega^4+omega^2)(5omega^3+omega+omega^2)

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)]

If omega is a complex cube root of unity,show that ([1 omega omega^(2)omega omega^(2)1 omega^(2)1 omega]+[omega omega^(2)1 omega^(2)1 omega omega omega^(2)1])[1 omega omega^(2)]=[000]