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

$\mathrm{S}=\{\mathrm{z} \in \mathrm{C} /|\mathrm{z}-1+\mathrm{i}|=1\}$ represents
  1. a circle with centre $(-1,1)$ and radius 1 unit
  2. a circle with centre $(1,2)$ and radius 5 units
  3. a circle with centre $(1,-1)$ and radius 1 unit
  4. 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

Asked in: AP EAMCET 2023 (15 May Shift 2)

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