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GATE 2020 ME (ME1) – Question 14

Engineering Mathematics · Complex Variables: Analytic functions, Cauchy-Riemann equations, integral theorem, Taylor and Laurent series · 1 mark · Multiple choice

Which function f(z) of the complex variable z is NOT analytic at all points of the complex plane?

  1. $f(z)=z^2$
  2. $f(z)=e^z$
  3. $f(z)=\sin z$
  4. $f(z)=\log z$

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Correct answer: (D) $f(z)=\log z$

Explanation

Polynomials, the exponential, and sine are entire functions. The complex logarithm is singular at zero and requires a branch choice; no branch is analytic on the entire complex plane. **Answer: D.**