The example Draw a Mandelbrot set fractal in C# explains how to draw a Mandelbrot set by iterating the equation:

    Zn = Zn-12 + C

Where Z_n and C are complex numbers. The program iterates this equation until the magnitude of Z_n is at least 2 or the program performs a maximum number of iterations.

That example tracks the numbers' real and imaginary parts in separate variables. This example uses a Complex class to manage the complex numbers more easily and intuitively. The following code shows the program's main loop.

Complex Z = Z0;
Complex C = new Complex(ReaC, ImaC);
int clr = 1;
while ((clr < MaxIterations) &&
       (Z.MagnitudeSquared < MAX_MAG_SQUARED))
{
    // Calculate Z(clr).
    Z = Z * Z + C;
    clr++;
}

See the code for details about how the Complex class works. The example Extend the complex number class to work with real numbers in C# describes some of the features of a class that is similar (although not exactly the same).