Complex numbers
Traditionally the complex numbers are visualized on the complex plane. We measure the real part of the complex numbers on the horizontal axis, and the imaginary part on the vertical one. A complex number can also be characterized by its absolute value (or modulus or magnitude) and its angle (or argument or phase).
The complex plane.
So to show a complex number one needs 2 dimensions.
Now we would like to plot complex valued functions of one complex variable. But to be able to do so—to be able to visualize a point together with the function value at that point—we would need 2+2=4 dimensions.
Still, throughout the years many ideas have risen for making the 2 dimensions available on our paper sheets and monitors sufficient to plot complex functions. In the section of Other methods we shall exhibit a couple of these.
But for now, our aim is to demonstrate the 'colorful' method. What if we would assign colors to the function values (as the 3rd and 4th dimensions)?