Here are some applications of complex numbers
- Quadratic equation can only be solved if is a complex number. The solution comes from the fact that , thus .
- When eigenvalues of a square matrix is a complex number, the behavior of the system is oscillating. This behavior can be understood because a complex number can be seen as superposition of trigonometric functions that has oscillating behavior, .
- Fourier series and Fast Fourier Transform (FFT) that often used for sound and digital image processing, adaptive filter, and many other applications are relied heavily on complex number. Fourier series formula is .
- Fractal is an iterated map of an original shape. Many well-known fractals such as Mandelbrot Set Fractal and Julia Set Fractal are based on quadratic transformation of complex number. In this tutorial, I also show how to make fractal geometry using complex linear transformation.
- Rigid body transformation (scaling, translation and rotation) is done using complex linear transformation .