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Manipal MET2017MathematicsComplex Number

If is an imaginary cube root of 1 , then (1+ - ^2 )^5+ (1- + ^2 )^5 is equal to

Options

  1. A16
  2. B8
  3. C9
  4. D32

Correct answer

D. 32

Step-by-step solution

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

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