Consider the complex function f(z) = 2iz + 1 − i defined on the closed annulus 2 ≤ |z| ≤ 3.
(a) Use linear mappings to determine upper and lower bounds on the modulus of f(z) = 2iz + 1 − i. That is, find real values L and M such that L ≤ |2iz + 1 − i| ≤ M.
(b) Find values of z that attain your bounds in (a). In other words, find z0 and z1 such that |f(z0)| = L and |f(z1)| = M.
(c) Determine upper and lower bounds on the modulus of the function g(z) = 1/f(z) defined on the closed annulus 2 ≤ |z| ≤ 3.
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