The previous applet was trying to show how the limit of some function ([math]z_1z_2[/math], where the two are conjugates) can take different values depending on [i]how[/i] we approached [math]z=0[/math]. [br][br]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 [math]p[/math] from only two directions. However, in the previous applet we saw that it is possible to approach [math]z=0[/math] from many directions, say from [math]i[/math] or [math]-i[/math] on some kind of curve we create. Let us now introduce derivatives of complex functions.