If $ \begin{vmatrix} 2 & 3+i & -1 \\ 3-i & 0 & i -1 \\ -1 &-1 -i & 1 \end{vmatrix} = A + iB $

where i= $\sqrt{-1}$ ,  then what is A+B equal to?

If $A{}^2+B{}^2+C{}^2=0$, then what is the value of the following?

$\begin{vmatrix} 1& cosC& cosB\\ cosC&1&cosA \\ cosB&cosA&1 \end{vmatrix} $

If ω is a non-real cube root of unity, then what is a root of the following equation?$ \begin{vmatrix} x+1 & \omega & \omega^2 \\ \omega & x+\omega^2 & 1 \\ \omega^2 & 1 & x+\omega \end{vmatrix} = 0 $