If \( e^{i x}=\cos x+i \sin x \) and \( x+i y=\left|\begin{array}{c...
If \( e^{i x}=\cos x+i \sin x \) and \( x+i y=\left|\begin{array}{ccc}1 & e^{\pi i / 4} & e^{\pi i / 3} \\ e^{-\pi i / 4} & 1 & e^{2 \pi i / 3} \\ e^{-\pi i / 3} & e^{-2 \pi i / 3} & e^{-2 \pi i}\end{array}\right| \), then
(a) \( x=-1, y=\sqrt{2} \)
(b) \( x=1, y=-\sqrt{2} \)
(c) \( x=-\sqrt{2}, y=\sqrt{2} \)
(d) none of these
\( \mathrm{P} \)
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