# Complex Numbers

## Uses Of Complex Numbers

Complex numbers are needed for the fundamental theorem of **algebra**: Every polynomial equation, P(x) = 0, with complex coefficients has a complex root. For example, the polynomial equation x^{2} + 1 = 0 has no real roots. If one allows complex numbers, however, it has two: 0 + i and - i.

Complex numbers are also used in the branch of **mathematics** known as "functions of complex variables." Such functions can often describe physical situations, as in electrical **engineering** and **fluid dynamics**, which real-valued functions cannot.

## Resources

### Books

Ball, W.W. Rouse. *A Short Account of the History of Mathematics.* London: Sterling Publications, 2002.

Bittinger, Marvin L., and Davic Ellenbogen. *Intermediate Algebra: Concepts and Applications.* 6th ed. Reading, MA: Addison-Wesley Publishing, 2001.

Jourdain, Philip E. B. "The Nature of Mathematics." *The World of Mathematics.* Newman, James, ed. New York: Simon and Schuster, 1956.

Stein, Sherman K. *Mathematics, the Man-made Universe.* San Francisco: W. H. Freeman and Co., 1969.

J. Paul Moulton

## Additional topics

Science EncyclopediaScience & Philosophy: *Cluster compound* to *Concupiscence*Complex Numbers - Arithmetic, Graphical Representation, Uses Of Complex Numbers