# Difference between revisions of "Complex number"

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− | A '''complex number''' is a [[number]] composed of two parts - a [[Real number|real]] component and and [[Imaginary number|imaginary]] component, of the form <math>a + bi</math>, where ''a'' and ''b'' are real numbers and | + | A '''complex number''' is a [[number]] composed of two parts - a [[Real number|real]] component and and [[Imaginary number|imaginary]] component, of the form <math>a + bi</math>, where ''a'' and ''b'' are real numbers and <math>i^2 = -1</math>. |

Whereas the real numbers can be represented as all the possible points on an infinitely extended [[number line]], to represent all the complex numbers requires the use of a two dimensional coordinate system, usually with the real components on the horizontal axis (the ''abscissa'') and the imaginary components on the vertical axis (the ''ordinate''). | Whereas the real numbers can be represented as all the possible points on an infinitely extended [[number line]], to represent all the complex numbers requires the use of a two dimensional coordinate system, usually with the real components on the horizontal axis (the ''abscissa'') and the imaginary components on the vertical axis (the ''ordinate''). |

## Revision as of 18:52, 19 December 2007

A **complex number** is a number composed of two parts - a real component and and imaginary component, of the form , where *a* and *b* are real numbers and .

Whereas the real numbers can be represented as all the possible points on an infinitely extended number line, to represent all the complex numbers requires the use of a two dimensional coordinate system, usually with the real components on the horizontal axis (the *abscissa*) and the imaginary components on the vertical axis (the *ordinate*).

The complex numbers form an algebraically closed field but do not permit a non-trivial ordering that is preserved under operations. They are the algebraic closure of the real numbers.

### In popular culture

In Yvgeny Zamyatin's satirical novel *We*, the narrator's psychological distress at contemplating the concept of complex numbers becomes a metaphor for the limitations of totalitarian systems of thought.