Question:

Show using a suitable contour that the complex logarithm function is defined by:

What I did was i used the contour so that:

I've reached here and now I'm absolutely stuck. What do i do next?

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- May 22nd 2011, 01:37 PMgarunasComplex Logarithm Function
**Question:**

Show using a suitable contour that the complex logarithm function is defined by:

What I did was i used the contour so that:

I've reached here and now I'm absolutely stuck. What do i do next? - May 23rd 2011, 03:28 AMOpalg
The formula is valid for an integral over the positive real line or the negative real line, but it does not work for integrals along complex contours.

I think that the easiest way to do this question is to use a different contour, namely one that goes along the real axis from 1 to |z| and then around a circular arc from |z| to z. The integral along the straight line segment will then give you without any difficulty. For the circular arc, write and parametrise the path by Then

- May 23rd 2011, 05:46 AMgarunas
Absolutely amazing!! Cheers!