Taylor Series: Can't quite work it out!

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

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hi wizard147!

(try using the X2 button just above the Reply box )
 Quote by wizard147 z* = -iR + R2/(z-iR) and my lecturer says that using the taylor series we get, z* = -iR + iR(1+ z/iR + ...)
you just have to fiddle around with it a little
z* = -iR + R2/(z-iR)

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

= -iR + iR/(z/iR - 1) …
hmm, there's a sign wrong somewhere

 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

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Taylor Series: Can't quite work it out!

yup! …
i think i got confused about whether the last "i" was on the top or the bottom of iR/z/iR !
thanks!

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