Equation of Circle in Complex Plane/Examples/z (conj z + 2) = 3/Mistake

Source Work

 * Chapter $1$: Complex Numbers
 * Supplementary Problems: Graphical Representation of Complex Numbers. Vectors: $71 \ \text {(d)}$

Mistake

 * ''Describe and graph the locus represented by each of the following:
 * ... $\text (d)$ $z \paren {\overline z + 2} = 3$


 * Ans. ... $\text (d)$ circle, ...

Correction
Working through in the direction one would go when trying to demonstrate the locus is a circle:

While it looks like the result follows from Equation of Circle in Cartesian Plane:


 * Equation of Circle in Complex Plane-Example-z (conj z + 2) = 3.png

it does not, because $y$ is real.

Otherwise, the circle would have center $\tuple {-1, -i} \notin \R^2$.