The value of cosπ2+isinπ2·cosπ4+isinπ4·cosπ8+isinπ8······∞
1
0
-1
None of these
Explanation for correct option
Given function is cosπ2+isinπ2·cosπ4+isinπ4·cosπ8+isinπ8······∞
We know that eiθ=cosθ+isinθ
∴cosπ2+isinπ2·cosπ4+isinπ4·cosπ8+isinπ8······∞=eiπ2.eiπ22.eiπ23······∞=eiπ21+12+122+...∞
We know that the sum of infinite GP series is a1-r
∴eiπ21+12+122+...∞=eiπ211-12=eiπ2·2=eiπ=cosπ+isinπ=-1+i·0=-1
Hence the correct option is OptionC