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CTID17
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Homework Statement
Find the Laurent series at z0=i, which is convergent in the annulus A ={z:0<|z-i|<51/2 } of
1/[(z-i)(z-2)]
Homework Equations
The Attempt at a Solution
|z-i|/51/2 <1
i make
1/[(z-i)(z-2)] = 1/[51/2 (z-i)((i-2)/51/2 + (z-i)/51/2 )
now how do i make it so that i have 1-(z-i)/51/2 to use the binomial series?
Is this a right approach to this type of questions? I could use partial factions to get
1/(2-i)*[1/(z-2)-1/(z-i)] but again i don't know how i can take advantage of |z-i|/51/2 <1 to use in the binomial series.
Thanks in advance.