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Problem 2 This problem explores the behavior of the exponential ez = exp (2) and the principal logarithm Log(z). Be sure to carefully label your drawings. (a) In one plane, draw the closed second quadrant Q2 along with the first three terms of the sequences defined by an = Inn and by = 1 + i(an/4). Next, let f(2) = ez and in another plane draw f(Q2) along with the first three terms of f(an) and f(bn). Does either limn-+0 f(an) or limn +0 f(bn) exist? (b) In one plane, draw D[0, 1]\\ {0} (a closed "punctured" disk) along with the first three terms of the sequences defined by an = 2el(*-m) and qn = 3el("+in). Next, let g(2) = Log(z) and in another plane draw g(D[0, 1]\\ {0} ) along with the first three terms of g(2) and g(wn). Determine both limn + g(Zn) and lim, +. g(Wn). (c) Prove that Log(z) is discontinuous on Ro , the nonpositive real axis