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AP EAMCET20227 Jul 2022Evening ShiftMathematicsComplex NumberActual

If 1, , ^2 denote the cube roots of unity, then the value of (1- + ^2 )^5+ (1+ - ^2 )^5 is

Options

  1. A32 ^2
  2. B32
  3. C-32
  4. D32

Correct answer

D. 32

Step-by-step solution

aligned & 1+ + ^2=0 & (1- + ^2 )^5+ (1+ - ^2 )^5 & =(-2 )^5+ (-2 ^2 )^5 & =-32 ( ^5+ ¹⁰ )=-32 ( ^2+ )=32 aligned

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