5. Use the function f(z) = z to show that in Exercise 4 the condition f(z) does not equal 0 anywhere in P is necessary in order to obtain the result of that exercise. That is, show that |f(z)| can reach its minimum value at an interior point when that minimum value is zero.
Please see the attached file for Exercise 4 and the fully formatted problem.© BrainMass Inc. brainmass.com March 4, 2021, 6:12 pm ad1c9bdddf
Proof. Consider the function f(z)=z and a closed bounded region , namely, a unit disk. Obviously, is continuous and ...
The Minimum Value of a Closed, Continuous Analytic Function is investigated.