The GATE Grind

GATE 2019 EC – Question 11

Engineering Mathematics · Complex Analysis · 1 mark · Multiple choice

Which one of the following functions is analytic over the entire complex plane?

  1. $\ln(z)$
  2. $e^{1/z}$
  3. $\dfrac{1}{1-z}$
  4. $\cos(z)$

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Correct answer: (D) $\cos(z)$

Explanation

$\ln z$ has a branch cut, $e^{1/z}$ has an essential singularity at $0$ and $\frac1{1-z}$ has a pole at $z=1$. $\cos z$ is entire.