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# Cauchy-Goursat - is this O.K? Watch

1. Hey, just wondering how you might answer this (and if my way is o.k?)

Question is: show that the integral around C (=|z| =1) of f(z) dz =0 where

The section before is about the cauchy-Goursat T, but my answer is:

the function can be split as:

So, as 1/2 is analytic everywhere, and (3/4)(1/(z+3/2)) is analytic within C, both =0 by the Cauchy-Goursat T.

OR, working out the integrals, we get:

and the 2nd one is:

my question really is, given the phrasing of the question: "show that..", and not: "show that, by the C-G Theorem..."

am i correct in quoting the theorem, then working the integral out to show it?
2. What I'd have done is shown that the premises of CG-thm are true. The theorem the of course does the rest of the work. It's asking you to show something; giving a condition like "by the --- theorem" means it obviously wants you to use that, but it doesn't mean you shouldnt use the theorem because it hasnt ask for it! I wouldnt think there would be any need to show it onced proved theorem-wise.

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Updated: July 4, 2014
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