Complex numbers and plane geometry

Abstract

The representation of complex numbers as points of the Euclidean plane naturally leads to a two-way interaction between geometry and numbers. The geometry of the plane has a very deep influence in the study complex analytic functions. In this article, we illustrate the other way aspect by a few simple-minded application of complex numbers to give elegant solutions of problems in plane geometry, such as Ptolemy’s Theorem, Euler-line and Nine-point Circle Theorem.