Let integers a, b ∈[-3,3] be such that a + b ≠ 0. Then the number of all possible ordered pairs (a, b), for which |(z-a)/(z+b)|=1 and |z+1, ω, ω^2;…

Let integers $\displaystyle \mathrm{a}, \mathrm{b} \in[-3,3]$ be such that $\displaystyle \mathrm{a}+\mathrm{b} \neq 0$. Then the number of all possible ordered pairs (a, b), for which $\displaystyle \left|\frac{z-a}{z+b}\right|=1$ and $\displaystyle \left|\begin{array}{ccc}z+1 & \omega & \omega^2 \\ \omega & z+\omega^2 & 1 \\ \omega^2 & 1 & z+\omega\end{array}\right|=1, z \in \mathrm{C}$, where $\displaystyle \omega$ and $\displaystyle \omega^2$ are the roots of $\displaystyle x^2+x+1=0$, is equal to $\displaystyle \_\_\_\_$.