Some Elementary Uses of Complex Numbers

Abstract

A special infinite series of real numbers which appeared in a comic strip is summed. Some of the techniques used are standard in complex calculus, but are now applied in a different context. Two other basic problems where complex numbers are useful are described. One, the solution of cubics is well known. The other, an extension of Ptolemy’s Theorem on cyclic quadrilaterals to general quadrilaterals, is an old result of Bretschneider, but the use of complex numbers to obtain this result seems to be new.