Texas College Mathematics Journal

Vol. 1 (2005), pp. 1-4.

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Means of Complex Numbers

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Barbara A. Sexton** and Julie C. Jones**

**MSC (2000):** Primary 30A99

**Key words:** mean, complex numbers

**Abstract: **There are many ways to find means of positive real numbers.
In this paper, we propose a definition of a mean of complex numbers. We use this
definition to show that the formula for geometric mean can be extended to
complex numbers. We also show that many other common methods of averaging real
numbers, such as the harmonic mean, the arithmetic mean, the heronian mean, the
logarithmic mean, the contraharmonic mean, and the power mean, cannot be
extended to complex numbers.

Department of Mathematics and Statistics, Sam Houston State University,
Huntsville, TX 77341-2206

e-mail: barbaras_math@yahoo.com, julie@shsu.edu

Received by Editor: May 27, 2004 and, in revised form December 13,
2004.

Posted: January 1, 2005.

© Copyright 2005