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.

Sections in this article:

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

The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2024, Columbia University Press. All rights reserved.

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