If \[{{e}^{i\theta }}=\cos \theta +i\sin \theta ,\] then the value of \[\left| \begin{matrix} 1 & {{e}^{i\pi /3}} & {{e}^{i\pi /4}} \\ {{e}^{-i\pi /3}} & 1 & {{e}^{i2\pi /3}} \\ {{e}^{-i\pi /4}} & {{e}^{-i2\pi /3}} & 1 \\ \end{matrix} \right|\]is

If \[{{e}^{i\theta }}=\cos \theta +i\sin \theta ,\] then the value of

1.	If \[{{e}^{i\theta }}=\cos \theta +i\sin \theta ,\] then the value of \[\left\| \begin{matrix} 1 & {{e}^{i\pi /3}} & {{e}^{i\pi /4}} \\ {{e}^{-i\pi /3}} & 1 & {{e}^{i2\pi /3}} \\ {{e}^{-i\pi /4}} & {{e}^{-i2\pi /3}} & 1 \\ \end{matrix} \right\|\]is
A.	\[-2+\sqrt{2}\]
B.	\[2-\sqrt{2}\]
C.	\[-2-\sqrt{2}\]
D.	1
Answer» D. 1

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If \[{{e}^{i\theta }}=\cos \theta +i\sin \theta ,\] then the value of \[\left| \begin{matrix} 1 & {{e}^{i\pi /3}} & {{e}^{i\pi /4}} \\ {{e}^{-i\pi /3}} & 1 & {{e}^{i2\pi /3}} \\ {{e}^{-i\pi /4}} & {{e}^{-i2\pi /3}} & 1 \\ \end{matrix} \right|\]is

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