VI.1.2. Let G be a bounded region and suppose f is continuous on G and analytic on G. Show that if there is a constant c

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Vi 1 2 Let G Be A Bounded Region And Suppose F Is Continuous On G And Analytic On G Show That If There Is A Constant C 1 (37.02 KiB) Viewed 36 times

VI.1.2. Let G be a bounded region and suppose f is continuous on G and analytic on G. Show that if there is a constant c≥ 0 such that f(z)| = c for all z € (G) then either f is a constant function or f has a zero in G. HINT: Consider f(z)/c, apply the Maximum Modulus Theorem and the Minimum Principle (Exercises IV.3.6 and VI.1.1).