Complex analysis problem
Find $\int_\gamma z^{-1/2} dz$ where $\gamma $ is upper half of unit circle from 1 to -1
Please, help

Question

anonymous · Answer

i forget 
don't you so something like put $z(t)=e^{it}$ so $z'(t)=ie^{it}$ ?

loser66 · Answer

I have to use branch cut, my Prof said I can see z^(-1/2) as principal branch cut of z^(-1/2). I don't get what he meant

loser66 · Answer

$z^(-1/2) = e^{(-1/2) logz}$

anonymous · Answer

is upper half of unit circle from 1 to -1 means this right?|dw:1447556104302:dw|

loser66 · Answer

Yes

loser66 · Answer

But when using branch cut, the log is undefined on negative of real part, we don't have -1 on the curve, how to argue?

loser66 · Answer

|dw:1447556231668:dw|