(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

4. Let w = f(z) = [tex]i(\frac{1-z}{1+z})[/tex]. Show that f maps the open unit disk {z [tex]\in[/tex] C | z < 1} into the upper half-plane {w[tex]\in[/tex] C|Im(w) >0}, and maps the unit circle {z[tex]\in[/tex] C||z|=1} to the real line.

2. Relevant equations

I was given this hint:

"set w=[tex]i(\frac{1-z}{1+z})[/tex] and use the formula Im(w)= [tex]\frac{1}{2i}[/tex](w -[tex]\bar{w}[/tex])"

3. The attempt at a solution

This is cliche but, what does this mean in English? I've been trying to decipher some of this stuff, in order for me to know what to do, I must first understand what I'm being asked to do, so that would be my first request.

The second thought I have of this is that the hint given also doesn't mean much to me. So what exactly would be the topic I could read on to help me get more information on this concept I'm being tested on? I'm at a library right now, so if I were to pick up a book on complex variables, what topic more or less is this problem covering?

I need to be pushed on the right direction to solve this problem, right now I'm just more or less in the dark. The set notation is a bit cryptic for me. I get that z is an element of the set of complex numbers, but what exactly is it being said after the "|"?

Thanks!

And pardon the rough formatting.

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# Homework Help: Show that the given function maps the open unit disk into the upper half plane

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