InterviewSolution
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InterviewSolution
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Find the value of following expression:`[(1-cospi/(10)+isinpi/(10))/(1-cospi/(10)-isinpi/(10))]^(10)` |
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Answer» Correct Answer - `-1` Let `cos.(pi)/(10) - isin.(pi)/(10) = z` `rArr cos.(pi)/(10) + isin.(pi)/(2) = (1)/(z)` `rArr [(1-cos.(pi)/(10)+isin.(pi)/(10))/(1-cos.(pi)/(10) -isin.(pi)/(10))]^(10) =((1-z)/(1-(1)/(z)))^(10)` `={(-(z-1)z)/((z-1))}^(10)` `=(-z)^(10)` =`z^(10)` `=(cos.(pi)/(10) -isin.(pi)/(10))^(10)` `=cos pi -isin pi` `=-1` |
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