AP EAMCET2005MathematicsComplex Number
If is a non-real root of x^6=1 , then ^5+ ^3+ +1 ^2+1 is equal to
Options
- A^2
- B0
- C- ^2
Correct answer
C. - ^2
Step-by-step solution
Given that aligned & (x-1) (x^5+x^4+x^3+x^2+x+1 )=0 & x^5+x^4+x^3+x^2+x+1=0 & aligned [ roots are non-real] Since is a root of the equation (i) array ll & ^5+ ^4+ ^3+ ^2+ +1=0 & ^5+ ^3+ +1=- ( ^4+ ^2 ) & ^5+ ^3+ +1=- ^2 ( ^2+1 ) & ^5+ ^3+ +1 ^2+1 =- ^2 array