Find the value of following expression: `[(1-cospi/(10)+isinpi/(10))/(1-cospi/(10)-isinpi/(10))]^(10)`

Answer

`-1`

Explanation

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`