1. The problem statement, all variables and given/known data "Study the infinitesimal behavior of f at the point c. (In other words, use the conformal mapping theorem to describe what is happening to the tangent vector of a smooth curve passing through c.)" f(z) = 1/(z-1), c=i 2. Relevant equations |f'(c)| and arg f'(c) 3. The attempt at a solution I know what |f'(c)| is, d/dz is -1/(z-1)^2, and evaluates out to 1/2i. However, I'm not sure what exactly that's saying about the behavior. Does it mean it's shrinking on the imaginary axis by 1/2 ? Also, about the argument... this is something I can't quite wrap my head around. I've read in this math text, and the wiki entry on arguments, but I'm not quite sure I get it. The equation in this book is, the argument of z = |z|(cos(theta)+ i*sin(theta)) where |z| = sqrt(x^2+y^2). Thanks.