GATE ME 2020 Set 1 — Question 14
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Engineering Mathematics → Complex Variables → Analytic Functions
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Question
Which of the following function , of the complex variable , is NOT analytic at all the points of the complex plane?
Correct answer
(D) f(z) = log z
Solution
A function is analytic if it is differentiable at every point in its domain.
1. is a polynomial and is an entire function (analytic everywhere in the complex plane).
2. is an exponential function and is an entire function.
3. is a trigonometric function and is an entire function.
4. is not analytic at (where it is undefined) and is typically defined with a branch cut (e.g., along the negative real axis), making it non-analytic along that cut. Therefore, it is not analytic at all points of the complex plane.
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