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Taylor Series: Can't quite work it out!

  1. Apr 19, 2012 #1
    Hi Guys,

    Looking at some notes i have on conformal mapping and I have the following

    where z is complex and z* denotes its conjugate, R is a real number


    z* = -iR + R^2/(z-iR)

    and my lecturer says that using the taylor series we get,

    z* = -iR + iR(1+ z/iR + ...)

    I've been trying for ages but I can't get this, I'm probably doing something stupid.

    Anybody point me in the right direction? I'm getting confused with all these expansions!

    I'm doing the following:

    z* = -iR + R^2/z(1-iR/z)

    and using the formula (1-x)^-1 = 1 + x^2 + x^3 (reference to wiki)

    but it's not quite working! Hope you can help

    C
     
  2. jcsd
  3. Apr 19, 2012 #2

    tiny-tim

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    hi wizard147! :smile:

    (try using the X2 button just above the Reply box :wink:)
    you just have to fiddle around with it a little :wink:

    z* = -iR + R2/(z-iR)

    = -iR + R/(z/R - i)

    = -iR + iR/(z/iR - 1) …​

    hmm, there's a sign wrong somewhere :redface:
     
  4. Apr 20, 2012 #3
    Hi Tim,

    Thanks, I think when you factored out your i, and then multiplied top and bottom by i you would get

    -iR + iR/(1-z/iR)

    I could be wrong though! lol
     
  5. Apr 20, 2012 #4

    tiny-tim

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    yup! …

    i think i got confused about whether the last "i" was on the top or the bottom of iR/z/iR ! :biggrin:

    thanks! :smile:
     
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