Problem #WSP-5655

Problems Complex Numbers

Problem

Let \(A,B,C,D\) be points on the plane represented by complex numbers \(a,b,c,d\). Show that the segments \(AB\) and \(CD\) are perpendicular if and only if \[\frac{d-c}{b-a}=-\frac{\bar d-\bar c}{\bar b- \bar a}\]