Let f: C→ Cbe a holomorphic function. Assume there is a ro > 0 such that |f(2)| < |z|? for |2| > ro- (i) Show that f(3) (2) = 0 for all z E C. (ii) Show that f is a quadratic polynomial.

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Let f: C → Cbe a holomorphic function. Assume there is a ro > 0 such that
|f(2)| < |z|?
for |2| > ro-
(i) Show that f (3) (2) = 0 for all z E C.
(ii) Show that f is a quadratic polynomial.
Transcribed Image Text:Let f: C → Cbe a holomorphic function. Assume there is a ro > 0 such that |f(2)| < |z|? for |2| > ro- (i) Show that f (3) (2) = 0 for all z E C. (ii) Show that f is a quadratic polynomial.
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