Some elementary uses of complex numbers (Q619446)

The author gives three examples of places where complex numbers can be used with profit in high school and early college mathematics. The rather known example of the general solution of cubic is related to a factoring problem which is interesting in its own right. A summation problem of infinite series, which the author found in a comic strip, is related to an expansion of a trigonometric function by Euler. The extension of Ptolemy's Theorem on cyclic quadrilaterals to general quadrilaterals is done by the use of complex numbers. This is a new derivation of a result found by C. A. Bretschneider (1808-1878) in 1842 (Grunert's Archiv).