If \[{{x}_{r}}=\cos \left( \frac{\pi }{{{2}^{r}}} \right)+i\sin \left( \frac{\pi }{{{2}^{r}}} \right)\], then\[{{x}_{1}}.{{x}_{2}}......\infty \]is [RPET 1990, 2000; BIT Mesra 1996; Karnataka CET 2000]

If \[{{x}_{r}}=\cos \left( \frac{\pi }{{{2}^{r}}} \right)+i\sin \lef

1.	If \[{{x}_{r}}=\cos \left( \frac{\pi }{{{2}^{r}}} \right)+i\sin \left( \frac{\pi }{{{2}^{r}}} \right)\], then\[{{x}_{1}}.{{x}_{2}}......\infty \]is [RPET 1990, 2000; BIT Mesra 1996; Karnataka CET 2000]
A.	\[-3\]
B.	\[-2\]
C.	\[-1\]
D.	0
Answer» D. 0

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If \[{{x}_{r}}=\cos \left( \frac{\pi }{{{2}^{r}}} \right)+i\sin \left( \frac{\pi }{{{2}^{r}}} \right)\], then\[{{x}_{1}}.{{x}_{2}}......\infty \]is [RPET 1990, 2000; BIT Mesra 1996; Karnataka CET 2000]

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