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