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AP EAMCET202319 May 2023Morning ShiftMathematicsComplex NumberActual

If z₁=2+3 i, z₂=4-5 i and z₃ are are three points in the Argand plane such that 5 z ₁+ xz ₂+ yz ₃=0(x, y R ) and z₃ is the midpoint of the segment joining the points z ₁ and z ₂ then x + y =

Options

  1. A-5
  2. B0
  3. C4
  4. D-1

Correct answer

A. -5

Step-by-step solution

z₃= z₁+z₂ 2 =3-i Now, 5 z₁+x z₂+ yz ₃=0 aligned & (10+4 x+3 y)+i(15-5 x-y)=0 & 4 x+3 y=-10 (i) and 15-5 x-y=0 aligned From equations (i) and (ii), we get x=5, y=-10 x+y=5-10=-5

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