Originally Posted by

**HallsofIvy** Sander and andrew2322 are using the fact that |z- a| is the distance from the point z to the point a in the complex plane. |z+ 5|= |z- (-5)| so |z+ 5|= 4 is satisfied for all points whose distanced from -5 is equal to 4- in other words, the circle with center -5 and radius 4.

Also, you arrived at $\displaystyle (x+ 5)^2+ y^2= 16$ and then proceeded to multiply out the square, etc. You should not have done that. You should have recognized immediately that this is of the form $\displaystyle (x- a)^2+ (y- b)^2= r^2$, the equation of a circle with center (a, b) and radius r, with a= -5, b= 0, and r= 4.