GATE Engineering Mathematics: Complex Variables – Previous Year Questions

8 GATE previous year questions on Complex Variables (Engineering Mathematics, Biomedical Engineering) with answers and explanations, from every paper.

1. GATE 2020 BM Q26 (1 mark, Numerical answer) – Evaluate 12 j Cz(z-1)(z-2)\,dz for positively oriented circle z =3/2.
2. GATE 2020 BM Q61 (2 marks, Numerical answer) – Find the de Broglie wavelength in nm of an electron accelerated through 1 V, to two decimals. Use electron mass 9.11×10⁻³¹ kg,h=6.63×10⁻³⁴ J s and…
3. GATE 2022 BM Q36 (2 marks, Multiple choice) – Evaluate Cz3-93z-i\,dz in the complex z plane.
4. GATE 2023 BM Q48 (2 marks, Multiple select) – For f(z)=1/(z−1), which counterclockwise circular contours yield contour integral 2πj?
5. GATE 2023 BM Q58 (2 marks, Numerical answer) – Expand sin z as a Taylor series about z=0. What is the reciprocal of the coefficient of z³?
6. GATE 2024 BM Q11 (1 mark, Multiple choice) – Evaluate counterclockwise z =38\,dzz(z-2)(z-4).
7. GATE 2024 BM Q44 (2 marks, Multiple choice) – Using residues, evaluate -dx1+x4.
8. GATE 2025 BM Q42 (2 marks, Multiple select) – For real x, which statements about y= e(-ex) are correct?