If is a non-real root of the equation x^6-1=0 , then ^2+ ^3+ ^4+ ^5 +1 is equal to

Step-by-step solution

Since, is a non-real root of the equation x^6-1=0 . array lc & ^6-1=0 & ^6-1=0 -1 & ^6-1 -1 =0 & 1+ + ^2+ ^3+ ^4+ ^5=0 & (1+ )+ ^2(1+ )+ ^4(1+ )=0 & (1+ ) (1+ ^2+ ^4 )=0 array aligned & ^2+ ^3+ ^4+ ^5 +1 = ^2( +1)+ ^4( +1) +1 & = ( +1) ( ^2+ ^4 ) +1 & = ^2+ ^4=-1 [from Eq. (i)] aligned