In this article we try to answer a few questions. Where did the complex numbers start from? How are complex numbers defined? Where and how do we represent complex numbers? What is the Mandelbrot set? We know that the multitude of complex numbers is fantastic, but it is even more interesting that with the help of these numbers, ama-zing images can appear on the complex plane. Thanks to Gaston Julia and Benoît Man-delbrot, today it is possible to visualize a fractal set, which being colored according to an algorithm, we enjoy the eyes with extremely beautiful images. Mandelbrot's set, in addition to the interesting features it possesses, also has an aesthetic value, which cannot be denied.