Setting Up The Magic
The previous applet was trying to show how the limit of some function (, where the two are conjugates) can take different values depending on how we approached .
This is not entirely different from the definition of limits in the real plane. The most noticeable difference is that within the reals, we can approach a point from only two directions. However, in the previous applet we saw that it is possible to approach from many directions, say from or on some kind of curve we create. Let us now introduce derivatives of complex functions.