What Does the Complex Plane Mean?

Real numbers can be visualized as points along a number line. Since all complex numbers can be written as a sum of a real number and an imaginary number, it is necessary to have both a real and an imaginary number line to visualize complex numbers. If the number lines are inserted into a coordinate system, you can visualize complex numbers in the complex plane.

You can think of a complex number $z$ as a vector or a point within the complex plane. By writing the number $z$ in Cartesian form, $z=a+bi$, it is easy to place the number in the complex plane. The real part of $z$ tells you where $z$ lies along the real axis. You can therefore think about the real part as the first coordinate of $z$. Correspondingly, the imaginary part tells you where $z$ lies along the complex axis, and can be thought of as the second coordinate of $z$. The complex number $z$ can therefore be assigned the coordinates $\left(a,b\right)$ in the complex plane.