Engineering Mathematics-II Unit 4 – Complex Variable – Differentiation: important questions for AKTU
Unit 4 (Complex Variable – Differentiation) questions that AKTU repeats most often. This unit carries about 27 marks per paper. Start with the repeated questions, then the most asked topics.
Most repeated Unit 4 questions
- Find the harmonic conjugate of u = x³ − 3xy² + 3x² − 3y² and hence find the analytic function f(z) = u + iv. (7 marks, 2024, Analytic Functions) – also asked in 2019, 2022, 2023, 2025
- If f(z) = u + iv is analytic, and u − v = (e^y − cos x + sin x) / (cosh y − cos x), find f(z) such that f(π/2) = (3−i)/2. (7 marks, 2025, Analytic Functions) – also asked in 2022, 2023, 2024
- Define analytic function. Show that f(z) = |z|² is not analytic anywhere except at origin. (7 marks, 2024, Analytic Functions) – also asked in 2022, 2023, 2025
Most important Unit 4 topic
- Analytic Functions (Unit 4: Complex Variable – Differentiation) – asked 15 times in 2019, 2022, 2023, 2024, 2025
Most asked Unit 4 topics
- Analytic Functions – asked 15 times
- Conformal Mapping – asked 7 times
- Complex Variable Functions
More Unit 4 previous year questions
- Show that the following function is harmonic: h(x, y) = x² + xy − y² (2 marks, 2025, Analytic Functions)
- If f(z) = { x³y⁵(x+iy) / (x⁶+y¹⁰) ; z ≠ 0 and 0 ; z = 0 }, show that f(z) is not analytic at z = 0 even if Cauchy-Riemann equations are satisfied at origin. (7 marks, 2025, Analytic Functions)
- Show that f(z) = z|z| is nowhere analytic. (7 marks, 2025, Analytic Functions)
- Find the analytic function f(z) = u + iv given u + v = (x − y)(x² + 4xy + y²) using Milne's Thomson method. (7 marks, 2024, Analytic Functions)
- Show that the function f(z) = |z|² is not analytic at origin. (2 marks, 2023, Analytic Functions)
Unit 4 syllabus topics
- Complex Variable Functions
- Analytic Functions
- Conformal Mapping