Quote:

So I consulted several texts on complex analysis and found:

1- Some authors define, and explicitely state, that $\displaystyle ]\textit{i} = \sqrt{-1}$

2- Some authors define math]\textit{i}^2 = -1[/tex] and never bring up the subject of what i is.

3- Some authors don't seem to consider complex numbers at all, but teach it using only the geometric interpretation of i = (0, 1) in the 2-D plane. They seem to be only teaching geometry, although I didn't look into the texts thoroughly.

4- One author doesn't seem to consider complex numbers at all, but teaches it using only vectors in the plane. Again, I didn't look into the text thoroughly.

i do not know what texts you are referring to, or what goals those texts had in mind when they were dealing with complex analysis, so i cannot comment intelligibly on that. but i will say that complex numbers haven't always been popular. the notion of $\displaystyle i$ was as controversial as Cantors notion of "infinite sets can be of different sizes, one can be bigger than another and the line has as many points as the plane etc etc etc" once upon a time. depending on when these texts were written, it may have some lingering touches of that "timidness" to venture into the world of unknown math or math that many were not comfortable with at the time.