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## 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?

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- Thread starter player1_1_1
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- #1

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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?

- #2

Hurkyl

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- #3

michael.wes

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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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