Can you set up the integral?
What does Cauchy's integral formula tell you?
By the way, it's not clear if you meant or .
Q: Using Cauchy’s integral formula, compute the integral of g(z) over the circle of radius 3 centred at the origin, the contour integral being taken counterclockwise.
g(z) =z^3 + z^2 − 5/z − 2
i cant wrap my head around this formula or how to even begin solving it. all other examples had two 'poles' rather tha just (z-2)
any help will be much appreciated.
That's a long shot from what you had written. You do know that , right? Parentheses are not a luxury.
It's clear that the only singularity is at .
Now can you write in the form , where is holomorphic inside the contour? What does Cauchy's formula tell you about the integral of such a form along the contour?
Yes. No.
You need to review Cauchy's Integral formula (see post #4 here for example (in your question n = 1): http://www.mathhelpforum.com/math-he...uchys-thm.html)
I said in my earlier reply that yes your f(z) was correct and no your answer was not correct. Where has the above come from - it is nothing more than a re-statement of the question! Did you read the post I refered you to? You need to compare the given integral to Cauchy's Integral Formula and:
1. Identify f(z).
2. Identify .
Then you need to:
3. Evaluate .
4. Write down the answer.
I just don't see where you can be stuck .... What part of the above can you not do?