Complex Plane
We cannot plot complex numbers on a number line as we might real numbers. However, we can still represent them graphically. To plot a complex number like [latex]3-4i[/latex], we need more than just a number line since there are two components to the number. To plot this number, we need two number lines, crossed to form a complex plane.
complex plane
In the complex plane, the horizontal axis is the real axis and the vertical axis is the imaginary axis.
How To: Given a complex number, represent its components on the complex plane.
- Determine the real part and the imaginary part of the complex number.
- Move along the horizontal axis to show the real part of the number.
- Move parallel to the vertical axis to show the imaginary part of the number.
- Plot the point.
Because this is analogous to the Cartesian coordinate system for plotting points, we can think about plotting our complex number [latex]z=a+bi[/latex] as if we were plotting the point [latex](a, b)[/latex] in Cartesian coordinates. Sometimes people write complex numbers as [latex]z=x+yi[/latex] to highlight this relation.
