Complex numbers and complex variables
Gunning, Robert C. Department of Mathematics, Princeton University, Princeton, New Jersey.
Last reviewed:June 2021
- Geometric interpretation
- Real and imaginary parts
- Complex conjugates
- Power series
- Analytic functions
- Cauchy integral formula
- Isolated singularities
- Global properties
- Meromorphic functions
- Rational functions
- Analytic functions of several variables
- Related Primary Literature
- Additional Reading
A natural and extremely useful extension of the familiar real numbers. They can be introduced formally as follows. Consider the two-dimensional real vector space consisting of all ordered pairs (a1, a2) of real numbers. Geometrically this space can be identified with the ordinary Euclidean plane, viewing the real numbers a1, a2 as the coordinates of a point in the plane.
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