number: The Complex Numbers

Numbers of the form z = x + yi, where x and y are real and i = −1, such as 8 + 7i (or 8 + 7−1), are called complex numbers; x is called the real part of z and yi the imaginary part. The real numbers are thus complex numbers with y = 0; e.g., the real number 4 can be expressed as the complex number 4 + 0i. The complex numbers are in a one-to-one correspondence with the points of a plane, with one axis defining the real parts of the numbers and one axis defining the imaginary parts. Mathematicians have extended this concept even further, as in quaternions.

• Introduction
• The Natural Numbers
• The Integers and Rational Numbers
• The Real Numbers
• The Complex Numbers
• The Algebraic and Transcendental Numbers
• Bibliography

The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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