3 P LLL Show that if f and f are both analytic on a domain D then f is constant Solution A Kumjian Let D be a domain and let f be a complex valued function such that both f and fare analytic on D Then both Ref f f and Im f f f must also be analytic on D Since Ref and Im f are also both real valued it follows by the theorem on page 50 that both are constant Hence f Ref ilm f is constant