Can anyone help me with this pls?
How can you prove that the integral of f(z) around the contour z= 1 is 0
where f(z) is Log(z+5)
Thx
Because $\displaystyle \log (z+5)$ is analytic on $\displaystyle \mathbb{C} - (\infty,-5]$. This is a simply connected domain and Cauchy's theorem tells us that the integral over a (rectifiable) curve of an analytic function on a simply connected domain is zero.