4. (a) Verify that f(z) = e/ has exactly one singularity, namely z = 0. (b)...

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4. (a) Verify that f(z) = e¹/² has exactly one singularity, namely z = 0. (b) For a real number r > 0, let D, be the punctured disk Dr = { z € C: 0 < |z| <r}. Show that for any r> 0, the function ƒ(z) = e¹/² maps D, onto C - {0}. (Hint: Where does exp(z) = e² map the set {ZEC : |Z| > } } ?) (c) Use part (b) to show that there is no w EC such that the function 8w (2) = Sel/z W ifz #0 if z = 0 4. (a) Verify that f(z) = e¹/² has exactly one singularity, namely z = 0. (b) For a real number r > 0, let D, be the punctured disk Dr = { z € C: 0 < |z| <r}. Show that for any r> 0, the function ƒ(z) = e¹/² maps D, onto C - {0}. (Hint: Where does exp(z) = e² map the set {ZEC : |Z| > } } ?) (c) Use part (b) to show that there is no w EC such that the function 8w (2) = Sel/z W ifz #0 if z = 0