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JEE Main20244 Apr 2024Evening ShiftMathematicsComplex NumberActual

The area (in sq. units) of the region S= z C :|z-1| 2 ;(z+ z )+i(z- z ) 2, Im (z) 0 is

Options

  1. A7 3
  2. B7 4
  3. C17 8
  4. D3 2

Correct answer

D. 3 2

Step-by-step solution

Put z=x+i y|z-1| 2 (x-1)^2+y^2 4 ...(i) x-y 1 ...(ii) Im ( z ) 0 y 0 ...(iii) aligned & Required area & = Area of semi-circle - area of sector A & 1 2 (2)^2- 2 & = 3 2 aligned

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