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

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- Apr 9th 2008, 12:37 AMstillsoulsearchingComplex 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 - Apr 9th 2008, 12:47 AMstillsoulsearching
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? - Apr 9th 2008, 08:28 AMThePerfectHacker
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.