Cartesian form

We used the Cartesian form to define a complex number. To see why it is called Cartesian, notice we can also use an ordered pair of real numbers to represent the complex number z. The first number of the ordered pair will be the real part of the complex number, and the second number will be the imaginary part:

Given this, we can represent complex numbers on a Cartesian coordinate system since a and b are just real numbers. We will need to make a couple of modifications though.

We will replace the x axis with an axis for the real part of a complex number ( Re(z) ), and the y axis with an axis for the imaginary part of a complex number ( Im(z) ), like so:

Figure 6.1 – The complex plane

This is called the complex plane. Here is an example involving actual complex numbers:

Figure 6.2 – Complex numbers on the complex plane

Keep this in mind as we go through the basic operations of complex...