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MHT CET202122 Sep 2021Evening ShiftMathematicsComplex NumberActual

If is the complex cube root of unity, the (3+5 +3 ^2 )^2+ (3+3 +5 ^2 )^2=

Options

  1. A-1
  2. B0
  3. C4
  4. D-4

Correct answer

D. -4

Step-by-step solution

aligned & (3+5 +3 ^2 )^2+ (3+3 +5 ^2 )^2 & = (3+3 +3 ^2+2 )^2+ (3+3 +3 ^2+2 ^2 )^2 & = [3 (1+ + ^2 )+2 ]^2+ [3 (1+ + ^2 )+2 ^2 ]^2 & =(3(0)+2 )^2+ [3(0)+2 ^2 ]^2=4 ^2+4 ^4 & =4 ^2 (1+ ^2 )=4 ^2(- ) & =-4 ^2=-4 aligned

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