A) 0
B) - 1
C) 1
D) 2
Correct Answer: B
Solution :
Let\[\cos \frac{\pi }{10}-i\sin \frac{\pi }{10}=z\]and \[\cos \frac{\pi }{10}+i\sin \frac{\pi }{10}=\frac{1}{z}\] Therefore, \[{{\left( \frac{1-z}{1-\frac{1}{z}} \right)}^{10}}\]\[={{\left\{ \frac{-(z-1)z}{(z-1)} \right\}}^{10}}={{(-z)}^{10}}\] \[={{z}^{10}}={{\left( \cos \frac{\pi }{10}-i\sin \frac{\pi }{10} \right)}^{10}}\]\[=\cos \pi -i\sin \pi =-1\].
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