limit of complex function
I have a wonderful book that is (unfortunately) at home.
It even has intuitive examples.
I'll quote from it & pass the title & such on to you later.
The main "gist" of taking a limit of a complex function is quite similar to that of a real function, with the exception of the direction you approach the limit from.
For a real function, say f(x) = x, you can form the limit as you approach the value a
either from the left or from the right. If the function is analytic about a, the two limits are the same.
In complex functions, being analytic means that the limit is the same no matter how a is approached.
Imagine a small circle about a in the complex plane. Any point on the circle has a radius and an angle (amplitude and phase) relative to a.
As the radius shrinks to 0, we approach a.
If there is ANY dependence of the limit on the angle (or phase) that we approach from, the function is not analytic about the complex value a.