The Cauchy Integral Formula

1. Mar 28, 2012

AlBell

1. The problem statement, all variables and given/known data

Use Cauchy's integral formula to evaluate when
a) C is the unit circle
b) c is the circle mod(Z)=2

2. Relevant equations

I know the integral formula is

3. The attempt at a solution
for the unit circle I was attempting F(z)=sin(z) and Z0=∏/2, which would give a solution of 2∏i, however if this is the correct method I am unsure how to modify it for a larger unit circle as I thought the final result was independent of radius

2. Mar 28, 2012

Office_Shredder

Staff Emeritus
The integral formula requires the point z0 to be contained inside of the curve gamma that you are integrating around. Draw some pictures and you should see the difference between the two curves they are asking you to integrate on

3. Mar 28, 2012

AlBell

Ah so the unit circle wouldn't actually contain the point pi/2 whereas the circle mod(z)=2 would?

4. Mar 28, 2012

Office_Shredder

Staff Emeritus
That's right. So in the unit circle case you need to figure out something else that lets you calculate the integral

5. Mar 28, 2012

AlBell

Can I then use the integral theorem that says it will equal 0?

6. Mar 28, 2012

Office_Shredder

Staff Emeritus
That will work

7. Mar 31, 2012

AlBell

I'm a bit confused again, sorry!
I thought that the z-Pi/2 on the denominator of the integral means we just shift the origin of the circle to a new position?