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.Plot the number [latex]3-4i[/latex] on the complex plane.
The real part of this number is [latex]3[/latex], and the imaginary part is [latex]-4[/latex]. To plot this, we draw a point [latex]3[/latex] units to the right of the origin in the horizontal direction and [latex]4[/latex] units down in the vertical direction.
