Q48 / 160 · AP EAMCET 2024 (20 May Shift 1) · Mathematics

$S=\{z \in C /|z+1-i|=1\}$ represents

  • Correct answer
    A
    the circle with centre at $(-1,1)$ and radius 1 unit
  • B
    the circle with centre at $(1,-1)$ and radius 1 unit
  • C
    the closed circular disc with centre at $(1,-1)$ and radius 1 unit
  • D
    the closed circular dise with centre at $(-1,1)$ and radius 1 unit

Solution

$S=\{z \in C \| z+1-i \mid=1\} \Rightarrow|z+1-i|=1$ $\Rightarrow|(x+1)+i(y-1)|=1 \Rightarrow(x+1)^2+(y-1)^2=1$ Which is circle with center at $(-1,1)$ and radius 1 unit.

Hence, the correct answer is option: 'A'.

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