(6) If $f$ is analytic on $|z| \le 1$ and is zero on the circle $|z| = 1$ then $f$ must be the zero function.
Added by Chelsey M.
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Step 1: By the identity theorem for analytic functions, if a function f is analytic on a domain D and f(z) = 0 for all z in a set that has a limit point in D, then f(z) = 0 for all z in D. Show more…
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