Some Elementary Uses of Complex Numbers

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...

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Bibliographic Details
Published in:Computational methods and function theory 2011, Vol.10 (2), p.579-584
Main Author: Askey, Richard
Format: Article
Language:English
Subjects:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Online Access:Get full text
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Summary: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.
ISSN:1617-9447
2195-3724
DOI:10.1007/BF03321781