GATE EE 2016 Set 2 — Question 16
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Engineering Mathematics → Complex Variables → Analytic Functions
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Question
Consider the function where is a complex variable and denotes its complex conjugate. Which one of the following is TRUE?
Correct answer
(B) f(z) is continuous but not analytic
Solution
1.Let . Then .
2..
3.We can write , where and .
4.Continuity: Both and are polynomial functions of and , which are continuous everywhere. Therefore, is continuous.
5.Analyticity: For a function to be analytic, it must satisfy the Cauchy-Riemann equations: and .
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