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​​​​Which of the following complex functions is/are analytic on the complex plane?

  1. $f(z)=j \operatorname{Re}(z)$
  2. $f(z)=\operatorname{Im}(z)$
  3. $f(z)=e^{|z|}$
  4. $f(z)=z^{2}-z$
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