The problem is to sketch lines of constant u and v in the image plane for the function Log[(z+1)/(z-1)].
The Attempt at a Solution
In order to do this I have to get the expression into u+iv form, so that I can read off and manipulate the u and v aspects of the function. What I can't figure out is how to get this equation into u+iv form.
I know that for Ln[z], I can write Ln[reitheta] = Ln[r] + itheta. Then u=Ln[r] and v=theta. But having that added +1 in the natural log is really throwing me off. Does anyone have any ideas for how to get this into u+iv form? Is there some obvious rule for simplifying the logarithm of a sum that I'm forgetting?