A) \[-1\]
B) \[1\]
C) \[0\]
D) \[\sqrt{2}\]
E) \[-\sqrt{2}\]
Correct Answer: A
Solution :
\[\left( \cos \frac{\pi }{2}+i\sin \frac{\pi }{2} \right)\left( \cos \frac{\pi }{{{2}^{2}}}+i\sin \frac{\pi }{{{2}^{2}}} \right)....\infty \] \[=\cos \left( \frac{\pi }{2}+\frac{\pi }{{{2}^{2}}}+....\infty \right)+i\sin \left( \frac{\pi }{2}+\frac{\pi }{{{2}^{2}}}+....\infty \right)\] \[=\cos \left( \frac{\pi }{2}.\frac{1}{1-\frac{1}{2}} \right)+i\sin \left( \frac{\pi }{2}.\frac{1}{1-\frac{1}{2}} \right)\] \[=\cos \pi +i\sin \pi \] \[=-1\]You need to login to perform this action.
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