f(z) = (z+1)/(z-1)
What are the images of the x and y axes under f? At what angle do the images intersect?
z = x + iy
The Attempt at a Solution
This is actually a 4 part question and this is the part I don't understand at all really.
The first 2 parts were a) Where is f analytic? Compute f' for this domain. and b) Where is f conformal.
I concluded that f is not analytic because it isn't differentiable at z = 1. The derivative, d/dz = z/(z-1) - (z+1)/[(z-1)^2]. I said f' is conformal along the complex plane except where z = 1 as well. z=1 creates problems in the derivative, where you measure what is and isn't conformal and where. I'm not sure this information is relevant to the actual images though, but I thought I'd put it in anyway just in case.