Q46 / 160 · AP EAMCET 2023 (15 May Shift 2) · Mathematics

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

  • A
    a circle with centre $(-1,1)$ and radius 1 unit
  • B
    a circle with centre $(1,2)$ and radius 5 units
  • Correct answer
    C
    a circle with centre $(1,-1)$ and radius 1 unit
  • D
    an ellipse with centre $(1,-1)$

Solution

Since $|z-1+i|=1 \Rightarrow|z-(1-i)|=1$ So, $\mathrm{S}$ represent a circle with centre $(1,-1)$ and radius 1

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

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