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Consider the function $f,g:\mathbb C \rightarrow \mathbb C$ defined by $f(z) = e^z, g(z) = e^{iz}$. Let $S = \{z \in \mathbb C: \mbox{Re }z \in [-\pi, \pi] \}$. Then  

  1.  $f$ is an onto entire function.
  2. $g$ is a bounded function on $\mathbb C$.
  3. $f$ is bounded on $S$. 
  4. $g$ is bounded on $S$.
in Complex Analysis by Expert | 93 views

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