`1/(1+2omega)+1/(2+omega)-1/(1+omega)`=0

(1)/(a + omega) + (1)/(b+omega) +(1)/(c + omega) + (1)/(d + omega) =(1)/(omega) where, a,b,c,d, in R and omega is a complex cube root of unity then find the value of sum (1)/(a^(2)-a+1)

If A =({:( 1,1,1),( 1,omega ^(2) , omega ),( 1 ,omega , omega ^(2)) :}) where omega is a complex cube root of unity then adj -A equals

Simplify : (1- omega) (1- omega^(2)) (1- omega^(4)) (1- omega^(8))

Prove the following (1+ omega) (1+ omega^(2)) (1 + omega^(4)) (1 + omega^(8)) ….to 2n factors = 1

Prove the following (1- omega + omega^(2)) (1- omega^(2) + omega^(4)) (1- omega^(4) + omega^(8)) …. to 2n factors = 2^(2n) where , ω is the cube root of unity.

If omega is a complex cube roots of unity, then find the value of the (1+ omega)(1+ omega^(2))(1+ omega^(4)) (1+ omega^(8)) … to 2n factors.

if omega!=1 is cube root of unity and x+y+z != 0 then |[x/(1+omega),y/(omega+omega^2),z/(omega^2+1)],[y/(omega+omega^2),z/(omega^2+1),x/(1+omega)],[z/(omega^2+1),x/(1+omega),y/(omega+omega^2)]| =0 if

If omega!=1 is a cube root of unity and x+y+z!=0, then prove that |[x/(1+omega), y/(omega+omega^2),z/(omega^2+1)],[y/(omega+omega^2),z/(omega^2+1),x/(1+omega)],[(z)/(omega^2+1),x/(1+omega),y/(omega+omega^2)]|=0 if x=y=z

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

If omega is a cube root of unity and /_\ = |(1, 2 omega), (omega, omega^2)| , then /_\ ^2 is equal to (A) - omega (B) omega (C) 1 (D) omega^2