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JEE Main20245 Apr 2024Evening ShiftMathematicsComplex NumberActual

Let S₁= z C:|z| 5 , S₂= z C: Im ( z+1- 3 i 1- 3 i ) 0 and S₃= z C: Re (z) 0 . Then the area of the region S₁ S₂ S₃ is :

Options

  1. A125 12
  2. B125 4
  3. C125 24
  4. D125 6

Correct answer

A. 125 12

Step-by-step solution

S₁: x^2+y^2 25...(1) aligned & S₂: lm of z+(1- 3 i) (1- 3 i) 0 & lm of ( x+i y 1- 3 i +1 ) 0 & lm of ( (x+i y)(1+ 3 i) 4 ) 0 & 3 x+y 0 ...(2) & S₃: x 0 ...(3) & Area = 5 12 ( (5)^2 ) aligned

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