GATE XE (Engineering Sciences) 2025 - Question 18

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Section: Engineering Mathematics | Marks: 2

Let 𝑓(𝑧) be an analytic function such that 𝑅𝑒(𝑓′(𝑧)) = 3π‘₯2 βˆ’4π‘¦βˆ’3𝑦2, 𝑓(𝑖) = 0, 𝑓′(0) = 0, where 𝑖= βˆšβˆ’1. Then the value of 𝑓(1) is equal to

  • A. 4 + 2𝑖
  • B. 1 + 5𝑖
  • C. 1 βˆ’π‘–
  • D. 4 βˆ’2𝑖

Answer: B. 1 + 5𝑖

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