find the laurent series of [tex]f(x)=\frac{-2}{z-1}[/tex]+[tex]\frac{3}{z+2}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

for

1<|z|<2

i was by my teacher that the radius of convergence

is what smaller then the number which makes the denominator 0.

if

[tex]f(x)=\frac{1}{1-z}[/tex]

then

the radius is 1 and

because 1-1=0

so

it is analitical on

|z|<1

so if i apply the same logic

[tex]f(x)=\frac{-2}{z-1}[/tex]

1 still makes denominator 0

and

it is analitical on

|z|<1

but the correct answer is

it is analitical on

|z|>1

for

[tex]f(x)=\frac{3}{z+2}[/tex]

-2 makes denominator 0

so |z|<-2 (but its illogical because |z| is a positive numbe)

where is my mistake?

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# Homework Help: Laurent series question

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