Visual Basic 2010 (Windows) Guide
Fractals: Complex Numbers

Producing the types of fractal image shown on the previous page requires a very basic understanding of complex numbers. The image itself is based on the results of a series of operations on a complex number.

A complex number comes in the following form,

a + b i

In the above number, a and b are real numbers. The letter i represents what is called the imaginary part of the number. The letter i stands for the square root of -1.

Some examples of complex numbers are,

3 + 2i
2.4 + 0.5i
0 + 5i

Plotting Complex Numbers

You can plot a complex number on a graph by using the real component for the position on the x axis and the imaginary component for the position on the y axis.

complex number

The number is represented by either the point plotted on the graph or as a vector with a line drawn from the origin to that point.