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JEE Main20253 Apr 2025Morning ShiftMathematicsComplex NumberActual

Let z C be such that z^2+3 i z-2+i =2+3 i . Then the sum of all possible values of z^2 is

Options

  1. A19-2 i
  2. B-19-2 i
  3. C19+2 i
  4. D-19+2 i

Correct answer

B. -19-2 i

Step-by-step solution

z^2+3 i=z(2+3 i)-7-4 i z ^2- z (2+3 i )+7+7 i =0 aligned & z₁^2+z₂^2= (z₁+z₂ )^2-2 z₁ z₂ & =4-9+12 i-14-14 i & =-19-2 i aligned

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