1. ## Complex Variables

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

2. I know Log(z) is ln r + i (theta). But i dont know how that applies to this situation.

Also, do I solve it as a normal integral or use the Cauchy Goursat theorem to prove that its integral is zero?

3. Originally Posted by stillsoulsearching
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 $\log (z+5)$ is analytic on $\mathbb{C} - (\infty,-5]$. 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.