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Paragraph Let the origin O of the argand plane represents the home town of a person. Suppose the man travels 2 units in north-east direction to reach city A. Then he travels 1 unit in east direction to reach town B . From town B he starts to move along a circular path, in anticlockwise direction with centre O and radius OB , to reach to city C such that BOC is right angle. Finally he returns home by the shortest path

Options

  1. A16 5 + 16 5 i
  2. B2 5 + 2 5 i
  3. C16 5 + 2 5 i
  4. D- 8 5 + 14 5 i

Correct answer

D. - 8 5 + 14 5 i

Step-by-step solution

Solving |z-z₁ |= |z-z₃ | , we get z(-2-i)+ z (-2+i)=3...(i) Let z_p be the image of z₂ in (i) z_p(-2-i)+ z ₂(-2+i)=3 z_p= -8 5 + 14 5 i

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