Q.The number of distinct complex numbers $z$ satisfying the equation $\begin{vmatrix} z+1 & \omega & \omega^2 \ \omega & z+\omega^2 & 1 \ \omega^2 & 1 & z+\omega \end{vmatrix} = 0$, where $\omega$ is a cube root of unity ($\omega \ne 1$), is