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JEE Main20254 Apr 2025Evening ShiftMathematicsComplex NumberActual

Let the product of ₁=(8+i) +(7+4 i) and ₂=(1+8 i) +(4+7 i) be +i , i = -1 . Let p and q be the maximum and the minimum values of + respectively.

Options

  1. A140
  2. B130
  3. C160
  4. D150

Correct answer

B. 130

Step-by-step solution

aligned & ₁=(8 +7 )+i( +4 ) & ₂=( +4 )+i(8 +7 ) & ₁ ₂=8 ^2 +7 +32 + & 28 ^2 -8 ^2 -32 -7 & -28 ^2 +i ( ^2 +4 +4 . & +16 ^2 +64 ^2 +56 +56 & . +49 ^2 ) & ₁ ₂=0+i (65 ^2 +120 +65 ^2 ) & + =65+60 2 q & + . |_ =125 & + . |_ =5 aligned Ans. =125+5=130 option (2)

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