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

Explanation

To solve the problem, we need to find the number of distinct complex numbers \( z \) that satisfy the determinant condition given by:

\[
\Delta = \begin{vmatrix}
z + 1 & \omega & \omega^2 \\
\omega z + \omega^2 & 1 & 1 \\
\omega^2 & 1 & z + \omega
\end{vmatrix} = 0
...