I finally got my hands on a book on complex Analysis that is written for Mathematicians. (We really do need a "drooling" smiley.) Anyway, I have a brief question about a restriction made in the definition of a "smooth" curve. A curve isn't smooth at some value of the curve parameter t if $\displaystyle z^{\prime}(t) = 0$.

Why the restriction here? Does it have something to do with the argument of the complex number 0 being undefined?

-Dan