In algebra and calculus, the complex plane is the coordinate system in which complex numbers are graphed. The vertical axis is the imaginary axis, and the horizontal axis is the real axis. Basically, in the complex number of the form a+bi, (where the real part is a and the imaginary part is bi) you go a spaces on the real axis, and b spaces on the imaginary axis. The complex plane can also be expressed in the form of polar coordinates, in which the magnitude of the line is equal to the square root of a plus b, and the direction is a specified angle, as in normal polar coordinates.
Every complex number of the form a+bi has a complex conjugate, which for the standard form (a+bi) is a-bi. The complex number and it's conjugate can be represented on the complex plane.
Complex plane Facts for Kids. Kiddle Encyclopedia.