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On the coordinate plane, know the set of points representing complex numbers \(z\) satisfy \(\left| {z + 2i} \right| = 1\)is a circle. The center of that circle has coordinates.
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A. \(\left( {0;2} \right)\).
B. \(\left( { – 2;0} \right)\).
C. \(\left( {0; – 2} \right)\).
D. \(\left( {2;0} \right)\).
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The answer:
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Put \(z = x + yi\)with \(x,y \in \mathbb{R}\).
From hypothetical \(\left| {z + 2i} \right| = 1 \Rightarrow {x^2} + {\left( {y + 2} \right)^2} = 1\).
Hence the set of points representing complex numbers \(z\) is the circle with center \(I\left( {0; – 2} \right)\)radius \(R = 1\)