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Why 1/z dont have antiderivative?

  • #1
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0

Homework Statement


why [tex]\frac{1}{z}[/tex] dont have derivative? i know that [tex]( \log z )'=\frac{1}{z}[/tex] so why [tex]\int \frac{1}{z} \mbox{d} z[/tex] dont exist?


Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
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The answer lies in all of the details you haven't said -- things like the domain of the functions under consideration and such.
 
  • #3
michael.wes
Gold Member
36
0
I just did this on an assignment, so I can answer this question :D

Note that we usually talk about log(z) as being the principal branch; then it is only defined on the cut-plane. It turns out that you cannot define a function such that f'(z)=1/z on the whole complex plane. In other words 1/z does not have a primitive on all of C.
 

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