The correct option is A 1+√2
Given x8=1
The roots can be ei2kπ/8, k=0,1,2,⋯,7
Hence x=e0⋅i,eiπ/4,eiπ/2,ei3π/4,eiπ,ei5π/4,ei3π/2,ei7π/4
So, the roots with +ve real part are
e0⋅i,eiπ/4,ei7π/4
Hence, required sum is
e0⋅i+eiπ/4+ei7π/4
=cos0+cosπ/4+isinπ/4+cos(7π/4)+isin(7π/4)=1+1√2+i1√2+1√2−i1√2=1+√2