Question

3. Suppose f is an entire function. Show that any of the two criteria below imply that f is a constant function. (a) Imf(x) #0 for all 2 € C and Ref(is an entire function. [10] (b) -1 < Ref(x) < 1 for all z e C. [8]

Answer 1

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8.-1. leto ze se 94 -101 -1<ust -> UCL = è se a & Zec then flz) is constant flz) = utiv e fez) eeriv le en 1. kl I tue =eu elv U = lete

e that entire function e fez an is We know gf fre) is entire fu then also Liouvilles Theorem; An entire bounded function Constanta so e fez) is constant it is entire and bounded by is bounded Sletenge? There for consfaut. fez is