Complex numbers and plane geometry

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. Anant R Shastri is a Professor at IIT, Bombay. His research inerests are in algebraic topology and algebraic geometry. He is also keen in math education and music. This article is based on a talk given to an audience consisting mainly students of class IX and X, at Nehru Science Centre under the aegis of Bombay Association for Science Education and Bombay Math. Colloq. on 25th Jan. 2003. An earlier version of this article was published in Bona Mathematica, Vol.14 Nos.1–2, 2003.