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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 x2 + 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

KEY TERMS

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Complex number

—A number composed of two separate parts, a real part and an imaginary part, joined by a "+" sign.

Imaginary number

—A number whose square is a negative number.

Additional topics

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