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

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a circle with center (-1,1) and radius 1 unit

a circle with center (1,2) and radius 5 unit

a circle with center (1,-1) and radius 1 unit

an ellipse with center (1,-1)

answer is C.

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Detailed Solution

$| z - 1 + i | = 1$

$|x + i y - 1 + i| = 1$

$|(x - 1) + i (y + 1)| = 1$

${(x - 1)}^{2} + {(y + 1)}^{2} = 1$ represents a circle with center (1,-1) and radius 1 unit

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