Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematics investigating functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics, and in physics.
In mathematics the Mandelbrot set, named after Benoît Mandelbrot, is a set of points in the complex plane, the boundary of which forms a fractal. Mathematically the Mandelbrot set can be defined as the set of complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1 = zn2 + c remains bounded.
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