(C) The given equation is $|z - 1 + i| = 1$. This can be rewritten as $|z - (1 - i)| = 1$. Comparing this with the standard equation of a circle in th

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a circle with centre $(1, -1)$ and radius $1$ unit

(C) The given equation is $|z - 1 + i| = 1$. This can be rewritten as $|z - (1 - i)| = 1$. Comparing this with the standard equation of a circle in the complex plane,$|z - z_0| = r$,where $z_0$ is the centre and $r$ is the radius,we get $z_0 = 1 - i$ and $r = 1$. In Cartesian coordinates,$z_0 = 1 - i$ corresponds to the point $(1, -1)$. Thus,$S$ represents a circle with centre $(1, -1)$ and radius $1$ unit.

Class 11 Mathematics 4-1.Complex numbers Geometry of complex numbers

Medium

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

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

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4-1.Complex numbers

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