Eh, no. Basically, you define a number i such that √(-1), the square root of negative one, equals i. That's called an imaginary number because it doesn't "mesh" with normal (real) numbers, and is "outside" them; 1+i can't be reduced to a real number, for instance.
Then a complex number can be defined as any number a+bi, where a and b are real numbers, and i is as up there. So 1+i, 3+i/9, 4 (= 4 + 0i), and 10i (= 0 + 10i) are all complex numbers.
Hopefully that makes sense so far. Now the trickier part comes in when you multiply them. Since i = √(-1), i▓ = -1. Therefore, (a+bi)(c+di) = ac+adi+bci+bdi▓=ac+adi+bci-bd=(ac-bd)+(ad+bc)i. Because of the subtraction, you lose the guarantee you get with real numbers, that multiplying two positive numbers gets you a bigger positive number.
Now the Mandelbrot set can be defined like this: For each point on the plane (x,y), call x+yi "c" (so c = x+yi). Then, starting with z0
= 0, say zn
)▓ + c. So for the point (1,0), c = 1+0i = 1; z0
= 0; z1
)▓ + c = 0▓ + 1 = 1; z2
= 1▓+1 = 2; z3
= 2▓+1 = 5; etc. Now it should be pretty obvious that successively higher z values get farther and farther from zero. Because of this, we say that the point (1,0) "escapes". In contrast, (0,1) = 0+i = i results in the z sequence 0, i, -1+i, -i, -1+i, -i, etc. repeating, and never "escapes". We say that a point is in the Mandelbrot set if it does not
escape. And from this relatively simple rule, you get the incredible complexity of the set.
Make any sense?