Complex Plane

The complex plane is a geometric plane used to represent complex numbers.

• The horizontal axis is the real axis.
• The vertical axis is the imaginary axis.
• A complex number z = a + bi is represented by the point (a, b).

Representation of z in the complex plane

Let z = a + bi. The point representing z is (a, b).

                 Imaginary axis
                       ↑
                       |
                       |             • z = (a, b)
                       |            /|
                       |           / |
                       |          /  | b = Im(z)
                       |         /
                       |        /
                       O────────┴────────────────→ Real axis
                      (0,0)     a = Re(z)

The horizontal coordinate is Re(z) = a, and the vertical coordinate is Im(z) = b.