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The real part of an analytic function $f(z)$ where $z = x + jy$ is given by $e^{-y} \cos(x)$. The imaginary part of $f(z)$ is

  1. $e^{y} \cos( x )$
  2. $e^{-y} \sin( x )$
  3. $-e^{y} \sin ( x )$
  4. $-e^{-y} \sin (x  )$
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