Discussion
Consider the following statements about contour integration. 1. Cauchy's theorem needs analyticity inside as well as on the contour 2. A vanishing contour integral proves the integrand analytic inside 3. The residue theorem reduces to Cauchy's theorem when no singularity is enclosed
Answer: C
The first and third hold. The second reverses the implication: the integral of \( 1/(z^{2}-1) \) round \( |z| = 2 \) vanishes although two poles lie inside, the residues merely cancelling. A vanishing integral is therefore evidence of nothing on its own
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