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JEE Main20258 Apr 2025Evening ShiftMathematicsComplex NumberActual

Let A = [0,2 ]: 1+10 Re ( 2 +i -3 i )=0 . Then _ A ^2 is equal to

Options

  1. A21 4 ^2
  2. B8 ^2
  3. C27 4 ^2
  4. D6 ^2

Correct answer

A. 21 4 ^2

Step-by-step solution

aligned & 1+10 Re ( 2 +i -3 i )=0 & z + z =2 Re ( z ) & 2 + i -3 i + 2 - i +3 i =2 ( -1 10 ) & (2 ^2 -3 ^2 )+ (2 ^2 )- (3 ^2 ) ^2 +9 ^2 = -2 10 & 2 ^2 -3 ^2 ^2 +9 ^2 = -1 10 & 20 ^2 -30 ^2 =- ^2 -9 ^2 & 21 ^2 -21 ^2 =0 & 2 =0 & 2 = 2 , 3 2 , 5 2 , 7 2 & ^2= ^2 16 + 9 ^2 16 + 25 ^2 16 + 49 ^2 16 = 84 ^2 16 = 21 ^2 4 aligned

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