I'd like to know what is wrong in the following steps:
This will be 0, and I know for sure that this should be 2 PI i. What am I doing wrong?
PS: I know I can use other techniques such as residues and such, but I want to understand what I'm doing wrong when trying to integrate by hand.
What is the COMMON value of ?
Tonio
: Ok, so by the above you get 0, but in may all depend on what value of Log(z) you're choosing: remember that Log(z) is multivalued and the argument of its value is determined only up to a multiple of , so it may be this the reason why you think (or you were given or you read in the solutions sheet) that the value is . It can as well be any multiple of this, too.
Tonio
Oh, I think I see now...sometimes posters change a question they're given and they don't add information relevant: of course, the complex integral you want indeed equals and this is due to the fact I added as to my second post: after revolving around a circle around a zero of , indeed the integral since the value of the primitive function (complex logarithm, of course) adds to its argument!
Tonio