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AP EAMCET202421 May 2024Morning ShiftMathematicsComplex NumberActual

If is the cube root of unity a+b +c ^2 c+a +b ^2 + a+b +c ^2 b+c +a ^2 =

Options

  1. A2
  2. B-2
  3. C1
  4. D-1

Correct answer

D. -1

Step-by-step solution

aligned & a+b +c ^2 c+a +b ^2 + a+b +c ^2 b+c +a ^2 & a+b +c ^2 c+a +b ^2 + ^2 (a+b +c ^2 ) b ^2+c+a & = (1+ ^2 ) ( a+b +c ^2 c+a +b ^2 )=- (a +b ^2+c ) (c+a +b ^2 ) =-1 aligned

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