If `2w-1=2,` what is the value of `w^(2)-1`?

If omega is a complex cube root of unity, then what is the value of 1-(1)/((1+omega))-(1)/((1+omega^(2))) ?

if omega be the cube root of unit then what is the value of |[1,omega ,omega^2],[omega, omega^2,1],[omega^2,1,omega ]| ?

If 1, w, w^2 are the cube roots of unity, then find the value of (1-w+w^2) (1+w-w^2) .

If 1,omega,omega^(2) are cube roots of unity, then the value of (1+omega)^(3)-(1+omega^(2))^(3) is :

If omega = (-1+sqrt3i)/2 , find the value of |(1, omega, omega^2),(omega, omega^2, 1),(omega^2, 1 , omega)|

If omega ne 1 is a cube root of unity satisfying (1)/(a + w) + (1)/(b + w) + (1)/(c +w) = 2 w^(2) and (1)/(a + w^(2)) + (1)/(b + w^(2)) + (1) /(c + w^(2)) = 2w then the value of (1)/(a + 1) + (1)/(b + 1) + (1)/(c + 1) is

If omega_(1) is complex cube root of that (1)/(a+omega)+(1)/(b+omega)+(1)/(c+omega)=2 omega^(2) and (1)/(a+omega^(2))+(1)/(b+omega^(2))+(1)/(c+omega^(2))=2 omega then the value of (1)/(a+1)+(1)/(b+1)+(1)/(c+1)=

If omega_(1) is complex cube root of that (1)/(a+omega)+(1)/(b+omega)+(1)/(c+omega)=2 omega^(2) and (1)/(a+omega^(2))+(1)/(b+omega^(2))+(1)/(c+omega^(2))=2 omega then the value of (1)/(a+1)+(1)/(b+1)+(1)/(c+1)=