In the article on the argument principle on planetmath , it says that $\oint_C d\log|f(z)|=0$ since $|f(z)|$ is single-valued. Why does that follow, or can someone point me to a fuller explanation? I'm studying complex-analysis right now, but this result is not obvious to me. Thanks.
Why does $\oint_C d\log|f(z)|=0$?
2
$\begingroup$
complex-analysis
1 Answers
2
Since $\log|f(z)|$ is single-valued, we have $ \oint_Cd\log|f(z)|=\log|f(z)|\bigg|_A^A=0 $ where $A$ is any point on $C$.
-
0Oh, that's very obvious, thanks! – 2012-03-15