A) \[-3\]
B) \[-2\]
C) \[-1\]
D) 0
Correct Answer: C
Solution :
\[{{x}_{1}},{{x}_{2}},{{x}_{3}}.....\]upto\[\infty =\]\[\left( \cos \frac{\pi }{2}+i\sin \frac{\pi }{2} \right)\,\,\left( \cos \frac{\pi }{{{2}^{2}}}+i\sin \frac{\pi }{{{2}^{2}}} \right)\] upto .....\[\infty \] \[=\cos \left( \frac{\pi }{2}+\frac{\pi }{{{2}^{2}}}+..... \right)\]\[+i\sin \left( \frac{\pi }{2}+\frac{\pi }{{{2}^{2}}}+..... \right)\] \[=\cos \left( \frac{\frac{\pi }{2}}{1-\frac{1}{2}} \right)+i\sin \left( \frac{\frac{\pi }{2}}{1-\frac{1}{2}} \right)\]\[=\cos \pi +i\sin \pi =-1\].
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