Compute integral of:

Integral over C of 1/z dz

where C is the unit circle centered at some point z.

|z.| >2

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- Feb 28th 2010, 02:29 PMstumped765contour integrals
Compute integral of:

Integral over C of 1/z dz

where C is the unit circle centered at some point z.

|z.| >2 - Feb 28th 2010, 07:07 PMwowsomeme
well a unit circle in 1 not z= 2

try putting z into polar form and then do a contour integral - Mar 1st 2010, 12:05 PMstumped765
the center of the circle is at a point z, |z|>2 its just saying the unit circle is shifted from the origin..

- Mar 1st 2010, 12:08 PMwowsomeme
would it be written then |z-2|>2

- Mar 1st 2010, 12:59 PMHallsofIvy
Then use something like to differentiate it from the variable .

The**unit**circle about with radius 1 is and with a going from 0 to .

Then .

However, you should know that is analytic everywhere except where z= 0 which, with , means everywhere inside this contour. - Mar 1st 2010, 02:19 PMshawsend
Hi. Here's something fun to check your knowledge about contour integrals: pin the center of the unit circle at the point 2i. Now, drop it straight through the singular point of at the origin until the center rests at -2i. Now, how does the value of the integral change as the circle falls?