1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    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!

Homework Help: Complex analysis question I don't understand solution

  1. Dec 5, 2013 #1
    So I am self studying complex analysis using some notes online so here he is trying to figure the map of certain domain applied to a function I follow everything but the end I don't get in the end when he got Re(w) < 1 how did he get that ? is it just because Re(w) which is 1/2 and 0 in this case is always less than 1? or what I don't get it.

    f(S) = {w ∈ C : |w −1/2| > 1/2, Re(w) < 1}.

    Attached Files:

  2. jcsd
  3. Dec 5, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

  4. Dec 5, 2013 #3


    User Avatar
    Homework Helper

    Notice at the beginning of the 3rd page, the first criteria given is u<0 which was kind of neglected until the end.
  5. Dec 5, 2013 #4
    but why exactly 1 ? I don't see how would that make it the case... ? @ Mentallic

    Perok ???
  6. Dec 5, 2013 #5


    User Avatar
    Homework Helper

    Because u<0 which is Re(1/w)<0 was one of the criteria we found that needs to be true after we did the inversion z->1/w, but then we needed to do an expansion z->2z, and u<0 simply becomes u<2(0) which is still u<0, so nothing changes in that step while the circle did change. The final step is a translation of z->z+1 so if u<0 then this becomes u<0+1=1. Hence, Re(w)<1.
  7. Dec 5, 2013 #6
    Thank you makes sense.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted