Mathematics - Complex Number Question with Solution | TestHub

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