I know if $f$ is analytic in a simply connected domain D then for any closed loop in D this integral is 0. Is that enough to say yes to this question?
2026-03-25 11:16:34.1774437394
If $f(z)$ is analytic inside and on the circle $|z| = 2$, is $\oint_{|z|=2}f(z) = 0?$
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Yes, of course, since the closed disk centered at $0$ with radius $2$ is simply connected.