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AP EAMCET201822 Apr 2018Evening ShiftMathematicsComplex NumberActual

If is a complex cube root of unity, the [ 51+73 +87 ^2 73+87 +51 ^2 + 51+73 +87 ^2 87+51 +73 ^2 ]=

Options

  1. A1
  2. B-1
  3. C0
  4. D2

Correct answer

B. -1

Step-by-step solution

aligned & [ 51+73 +87 ^2 73+87 +51 ^2 + 51+73 +87 ^2 87+51 +73 ^2 ]¹⁵ & = [ array c 51 ^2+73 ^3+87 ^4 73+87 +51 ^2 1 ^2 + 51 +73 ^2+87 ^3 87+51 +73 ^2 1 array ]¹⁵ & = [ 73+87 +51 ^2 73+87 +51 ^2 ^3 + 87+51 +73 ^2 87+51 +73 ^2 ^2 ^3 ]¹⁵ & = ( + ^2 )¹⁵=(-1)¹⁵=-1 aligned

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