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JEE Main2006MathematicsComplex NumberActual

If z^2+z+1=0 , where z is a complex number, then the value of (z+ 1 z )^2+ (z^2+ 1 z^2 )^2+ (z^3+ 1 z^3 )^2+ + (z^6+ 1 z^6 )^2

Options

  1. A18
  2. B54
  3. C6
  4. D12

Correct answer

D. 12

Step-by-step solution

z^2+z+1=0 z= or ^2 so, z+ 1 z = + ^2=-1, z^2+ 1 z^2 = ^2+ =-1, z^3+ 1 z^3 = ^3+ ^3=2z^4+ 1 z^4 =-1, z^5+ 1 z^5 =-1 and z^6+ 1 z^6 =2 The given sum =1+1+4+1+1+4=12

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