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Inversion mapping of z

  1. Jan 18, 2012 #1
    1. The problem statement, all variables and given/known data
    Show that the inversion mapping w = f(z) = 1/z maps the circle |z - 1| = 1 onto the vertical line x = 1/2.


    2. Relevant equations



    3. The attempt at a solution
    z = a + ib
    w = x + yi = a^2/(a^2 + b^2) + ib^2/(a^2 + b^2)
    |z - 1| = |(a -1) + ib | = 1
    (a - 1)^2 + b^2 = 1
    a^2 + b^2 = 2ab

    Not sure what to do afterwards.
     
  2. jcsd
  3. Jan 18, 2012 #2
    Hint: The last equation is wrong. It should read [itex]a^2+b^2=2a[/itex], which makes your job a whole lot easier.
     
  4. Jan 18, 2012 #3
    Thanks! That was really easy.
     
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