Texas College Mathematics Journal
Vol. 1 (2005), pp. 1-4.

Means of Complex Numbers

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