TITLE: Geometric interpretation of $|\frac{z+i} {z-i}| =2$
QUESTION [6 upvotes]: Consider the equation
$$\left|\frac{z+i} {z-i}\right| =2$$
Solving it yields a circle, but I wonder if the equation itself has a geometric interpretation.

REPLY [6 votes]: Here is a sketch of what geometrically is going on:

NOTE
As AB is constant, the equation describes a circle known as the Circle of Apollonius.
https://en.wikipedia.org/wiki/Circles_of_Apollonius