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Argand diagram
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A diagram of the complex plane with horizontal real axis and vertical imaginary axis, showing a point labeled x + iy and dashed lines connecting it to coordinates x on the real axis and y on the imaginary axis. Figure 2: The complex number.
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A diagram of the complex plane with horizontal real axis and vertical imaginary axis, showing a point labeled x + iy and dashed lines connecting it to coordinates x on the real axis and y on the imaginary axis.
point in the complex plane A point in the complex plane. Unlike real numbers, which can be located by a single signed (positive or negative) number along a number line, complex numbers require a plane with two axes, one axis for the real number component and one axis for the imaginary component. Although the complex plane looks like the ordinary two-dimensional plane, where each point is determined by an ordered pair of real numbers (x, y), the point x + iy is a single number.

Argand diagram

mathematics
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History

Argand diagram, graphic portrayal of complex numbers, those of the form x + yi, in which x and y are real numbers and i is the square root of βˆ’1. It was devised by the Swiss mathematician Jean Robert Argand about 1806. A similar representation had been proposed by the Danish surveyor Caspar Wessel in 1797, but this was not generally known until later. One axis represents the pure imaginary numbers (those consisting of the yi portion only); the second represents the real numbers (x-values only). This permits the complex numbers to be plotted as points in the plane defined by the two axes, as shown in the figure.

The Editors of Encyclopaedia Britannica This article was most recently revised and updated by William L. Hosch.