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)

(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)

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

|{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}|=0 where omega is an imaginary cube root of unity.

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

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

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