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complex number

A complex number is a quantity of the form v + iw, where  v and w are real numbers, and i represents the unit imaginary numbers equal to the positive square root of -1. The set C of all complex numbers corresponds one-to-one with the set R R of all ordered pairs of real numbers.The set C  also corresponds one-to-one with the points on a geometric plane.

The set of complex numbers is two-dimensional, and a coordinate plane is required to illustrate them graphically.This is in contrast to the real numbers, which are one-dimensional, and can be illustrated by a simple number line.The rectangular complex number plane is constructed by arranging the real numbers along the horizontal axis, and the imaginary numbers along the vertical axis.Each point in this plane can be assigned to a unique complex number, and each complex number can be assigned to a unique point in the plane.

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Complex numbers are used in engineering, particularly in electronics. Real numbers are used to denote electrical resistance, imaginary numbers are used to denote reactance, and complex numbers are used to represent impedance.

This was last updated in May 2008

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