If `1/(a+omega)+1/(b+omega)+1/(c+omega)+1/(d+omega)=1/omega` where `a,b,c,d in R and omega` is cube root of unity then show that `sum 1/(a^2-a+1)=1`.

(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 omega ne 1 is a cube root of unity, then 1, omega, omega^(2)

If (omega!=1) is a cube root of unity then omega^(5)+omega^(4)+1 is

If w is an imaginary cube root of unity then prove that (1-w)(1-w^2)(1-w^4)(1-w^5)=9

What is sqrt((1+_(omega)^(2))/(1+_(omega))) equal to, where omega is the cube root of unity ?

Evaluate: | (1, 1, 1), (1, omega^2, omega), (1, omega, omega^2)| (where omega is an imaginary cube root unity).

Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega,omega)| where omega is cube root of unity.

find the value of |[1,1,1],[1,omega^(2),omega],[1,omega,omega^(2)]| where omega is a cube root of unity

If omega be an imaginary cube root of unity, show that: 1/(1+2omega)+ 1/(2+omega) - 1/(1+omega)=0 .