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AP EAMCET202318 May 2023Morning ShiftMathematicsComplex NumberActual

If z = x + iy represents a point in the Argand plane, then a point which is not in the region represented by |z-1+i| 2 is

Options

  1. A1-i 2
  2. B1
  3. C1-i 4
  4. Di

Correct answer

D. i

Step-by-step solution

|z-1+i| 2 | z -(1- i )| 2 (a) Let z₁= 1-1 2 then |z₁-(1-i) |= | (1-i) 2 |= 1 4 + 1 4 = | (1-i) 2 |= 1 4 + 1 4 = 1 2 2 z ₁ is in the region. (b) Let z₂=1 , then |z₂-(1-i) |=|i|=1 2 . z ₂ is in the region. (c) Let z ₃= 1- i 4 , then | z ₃-(1- i ) |= |- 3 4 (1-i) |= 3 4 2 2 aligned & (d) Let z₄=i then |z₄-(1-i) |=|i-1+i|=|2 i-1| & = 4+1 aligned = 5 >2 i is not in the region.

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