In mathematics, a complex plane is a geometric representation of a complex number established by a horizontal real axis and a vertical imaginary axis. It can be regarded as a Cartesian plane (real plane) with a specific algebraic structure. The real part of a complex number is represented by the displacement along the X axis, and the imaginary part is represented by the displacement along the Y axis.

The complex plane is sometimes called Algonplane because it is used in Algongraph. They are named after Jean-Robert Algon1768-1822, although they were first described by Caspar Wessel, a Norwegian-Danish land surveyor and mathematician (1745-1818). Algongraph is often used to represent the positions of poles and zeros of a function on a complex plane.

Establish a rectangular coordinate system to represent complex numbers. The plane is called the complex plane, the X axis is called the real axis, and the part of the Y axis except the origin is called the imaginary axis. The origin represents real number 0, and the origin is not on the imaginary axis. Every point on the complex plane has a unique complex number corresponding to it, and conversely, every complex number has a unique point corresponding to it, so the complex set C is one-to-one corresponding to the set of all points on the complex plane.

Complex number Z=a+bi, like real number pair (a, b), can establish a one-to-one correspondence with a point on the coordinate plane, so the coordinate plane that has established a one-to-one correspondence with all complex numbers is called the complex plane, also known as the Gaussian plane.