why [tex]\frac{1}{z}[/tex] don't have derivative? i know that [tex]( \log z )'=\frac{1}{z}[/tex] so why [tex]\int \frac{1}{z} \mbox{d} z[/tex] don't exist?
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.