## On the coordinate plane, know the set of points representing complex numbers (z) satisfying |z + 2i| = 1 is a circle. The center of that circle has coordinates. – Math book

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. $$\left( {2;0} \right)$$.

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 $$R = 1$$