1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Complex mapping question

  1. Apr 17, 2012 #1
    1. The problem statement, all variables and given/known data
    find linear fractional transformation from D={z:|Arg z| < [itex]\alpha[/itex]}, [itex]\alpha≤[/itex][itex]\pi[/itex] to the upper half plane

    2. Relevant equations

    3. The attempt at a solution

    The problem I am having here what exactly D is.. (visualizing it) D is just z such that |Arg z|≤[itex]\pi[/itex] right? so wouldn't that just be the entire complex plane? If we consider the Argument from 0 to [itex]\pi[/itex] and from 0 to -[itex]\pi[/itex] since |-[itex]\pi[/itex]|=[itex]\pi[/itex] Is this correct??
  2. jcsd
  3. Apr 17, 2012 #2
  4. Apr 17, 2012 #3
    I believe what this is saying is that you first select [itex]\alpha \leq \pi[/itex] and then form [itex]D := \left\{ z : \left| \mathit{arg} \ z \right| < \alpha \right\}[/itex]. This would not be the entire complex plane. I believe for say [itex]\alpha = \frac{\pi}{2}[/itex] would look like [itex]D = \left\{ z : \mathit{real} \ z > 0 \right\}[/itex].
  5. Apr 17, 2012 #4
    right but then if [itex]\alpha[/itex]=[itex]\pi[/itex] wouldn't it just be the entire plane? since if it is [itex]\pi[/itex]/2 then it is half of the plane..
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook