In algebra and calculus, the complex plane is used to help visualize complex numbers. The vertical line is called the imaginary axis, and the horizontal line is called the real axis. Any complex number can be written as a+bi, (a and b are real numbers, and i is the square root of -1). In the complex plane, 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 size of the line is equal to the square root of a squared plus b squared, and the direction is an angle.
Every complex number a+bi has a complex conjugate, which is a-bi. The complex number and it's conjugate can be represented on the complex plane.