If \( \omega \neq 1 \) is a complex cube root of unity, and
\[
x+i ...
If \( \omega \neq 1 \) is a complex cube root of unity, and
\[
x+i y=\left|\begin{array}{ccc}
1 & i & -\omega \\
-i & 1 & \omega^{2} \\
\omega & -\omega^{2} & 1
\end{array}\right|
\]
then
(a) \( x=-1, y=0 \)
(b) \( x=1, y=-1 \)
(c) \( x=1, y=1 \)
(d) \( x=0, y=0 \)
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