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GATE Mechanical 2024 | Question: 3

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​​​​​Let $f(z)$ be an analytic function, where $z=x+i y$. If the real part of $f(z)$ is $\cosh x \cos y$, and the imaginary part of $f(z)$ is zero for $y=0$, then $f(z)$ is

  1. $\cosh x \exp (-i y)$
  2. $\cosh z \exp z$
  3. $\cosh z \cos y$
  4. $\cosh z$
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