Let w be the complex number `cos(2pi)/3 + isin(2pi)/3`. Then the number of distinct complex numbers z satisfying `|(z+1, w, w^2),(2, z+w^2, 1),(w^2, 1, z+w)|=0` is equal

Let omega be the complex number cos((2pi)/3)+isin((2pi)/3) . Then the number of distinct complex numbers z satisfying Delta=|(z+1,omega,omega^2),(omega,z+omega^2,1),(omega^2,1,z+omega)|=0 is

Let omega be the complex number cos((2pi)/3)+isin((2pi)/3) . Then the number of distinct complex cos numbers z satisfying Delta=|(z+1,omega,omega^2),(omega,z+omega^2,1),(omega^2,1,z+omega)|=0 is

Let omega be the complex number cos((2pi)/3)+isin((2pi)/3) . Then the number of distinct complex cos numbers z satisfying Delta=|(z+1,omega,omega^2),(omega,z+omega^2,1),(omega^2,1,z+omega)|=0 is

Let omega be the complex number cos((2pi)/3)+isin((2pi)/3) . Then the number of distinct complex cos numbers z satisfying Delta=|(z+1,omega,omega^2),(omega,z+omega^2,1),(omega^2,1,z+omega)|=0 is

Let omega be the complex number cos((2pi)/3)+isin((2pi)/3) . Then the number of distinct complex cos numbers z satisfying Delta=|(z+1,omega,omega^2),(omega,z+omega^2,1),(omega^2,1,z+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

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

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