[1,omega,omega^(2)],[omega,omega^(2),1],[omega^(2),1,omega]=0

If omega is a complex cube root of unity.Show that Det[[1,omega,omega^(2)omega,omega^(2),1omega^(2),1,omega]]=0

Let omega be the complex number cos (2 pi)/(3)+i sin (2 pi)/(3) . Then the number of distinct complex number z satisfying [[z+1,omega,omega^(2)],[omega,z+omega^2,1],[omega^(2),1,z+omega]] = 0 is equal to

Evaluate the following determinants. [[1,omega,omega^2],[omega,omega^2,1],[omega^2,1,omega]]

|[1,omega,omega^2] , [omega, omega^2,1] , [omega^2,1,omega]|=0

Using properties, prove that |[1,omega,omega^2],[omega,omega^2,1],[omega^2,1,omega]|=0 where omega is a complex cube root of unity.

{[(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))]

(b) answer any one of the foll.: (i) prove without expanding |[1,omega,omega ^2],[omega ,omega ^2 ,1],[omega ^2,1, omega]|=0 wher w is an imaginary cube root of unity.

Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^2,1,x+omega]] =0

If omega is a complex cube root of unity then a root of the equation |[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^2,1,x+omega]|=0 is

Let omega be the complex number cos(2pi/3)+isin(2pi/3) Then the number of distinct complex numbers z satisfying abs[[z+1,omega,omega^2],[omega,(z+omega^2),1],[omega^2,1 ,z+omega]]=0 is equals to