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.