Solving Problems in Geometry by Using Complex Numbers

Someone once said that mathematics consists of finding new solutions to old problems and old solutions to new problems. Sometimes, however, it becomes necessary to revive old solutions for old problems. Approximately a hundred years ago C. A. Laisant and other mathematicians of that time used vector methods, with coordinates in the complex plane, to solve certain types of problems in geometry involving polygons having the same centroid, called concentric polygons. This method has been neglected, and it is almost forgotten today. It is the purpose of this article to attempt to revive this method by illustrating its effectiveness in solving certain types of problems in elementary geometry.