Some elementary uses of complex numbers
type: Item
instance of: scholarly article
title: Some elementary uses of complex numbers
zbMATH Open document ID: 1213.00036
DOI: 10.1007/BF03321781
author: R. Askey
published in: Computational Methods and Function Theory
publication date: 2011-01-25T00:00:00Z
review text: 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).
reviewed by: Reinhard Siegmund-Schultze
Mathematics Subject Classification ID: 00A35
Mathematics Subject Classification ID: 30-01
Mathematics Subject Classification ID: 40-01
Mathematics Subject Classification ID: 40-03
zbMATH DE Number: 5840925
zbMATH Keywords: use of complex numbers in teaching
zbMATH Keywords: Euler
zbMATH Keywords: summation of series
zbMATH Keywords: cubic equations
zbMATH Keywords: general quadrilaterals
MaRDI profile type: Publication
cites work: Q4315272
full work available at URL: https://doi.org/10.1007/bf03321781
OpenAlex ID: W2043268856
description: scientific article; zbMATH DE number 5840925