Here, α and β are the roots of the equation x2+x+1=0 α=
−1+√12−4
2
=
−1+√3i
2
and β=
−1−√3i
2
......(Usingx=
−b±√b2−4ac
2a
) α=ω and β=ω2 In equation x2−x+1=0 Roots =
1±√12−4
2
=
1±√3i
2
So, roots are −β and −α, i.e., −ω2 and −ω Sum of roots in quadratic equation x2−x+1=0 , is 1 Assume roots are α7 and β13 α7+β13=((−ω)7+(−ω2)13) =−((ω3)2+(ω3)8ω2) =−(ω+ω2) =−(−1) =1 Hence, option (1) is correct.