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AP EAMCET202021 Sep 2020Morning ShiftMathematicsComplex NumberActual

Geometrically, the set ( z C :|z-2-2 i| 1 ) represents

Options

  1. Aa closed circular disc with center at ((-2,-2) ) and with radius 1
  2. Ba closed circular disc with center at ((2,2) ) and with radius 1
  3. Ca closed circular disc with center at ((1,1) ) and with radius 0.5
  4. Da closed circular disc with center at ((-1,-1) ) and with radius 0.5

Correct answer

B. a closed circular disc with center at ((2,2) ) and with radius 1

Step-by-step solution

Given inequality is (|z-2-2 i| 1 ) Let (z=x+i y ), then we get ( aligned & & (x-2)^2+(y-2)^2 & 1 & & (x-2)^2+(y-2)^2 & 1 aligned ) The above inequality represents a closed circular disc with center at ((2,2) ) and with radius 1. Hence, option (b) is correct.

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