Complex plane

The complex plane represents each complex number as a point, with its real part on the horizontal axis and its imaginary part on the vertical axis.

Complex number: A number expressible as a real part plus an imaginary part. Each point is the geometric representation of one complex number.
Complex addition: Addition of complex numbers by separately adding their real and imaginary parts. On the plane, this operation is vector addition.
Argand diagram: A graphical representation of complex numbers as points or vectors in a plane. It is the standard diagrammatic form of the complex plane.
Real number line: A one-dimensional line on which each real number corresponds to a point. It is the horizontal axis alone, without the imaginary dimension.
Real part: The real component of a complex number, written as the coefficient of its non-imaginary term. It supplies a point’s horizontal coordinate.
Complex multiplication: Multiplication of complex numbers using the distributive law and i² = −1. Its geometric effect combines changes in distance from the origin and angle.
Complex function: A function whose inputs and outputs are complex numbers. Such functions map regions or curves of the plane to other parts of it.
Complex projective line: The complex plane together with one additional point at infinity. It extends the plane to include infinity and make it compact.
Imaginary part: The coefficient of the imaginary unit in a complex number. It supplies a point’s vertical coordinate.
Complex modulus: The nonnegative magnitude of a complex number, equal to its distance from zero. It measures the distance of a represented point from the origin.

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