GATE Engineering Mathematics: Complex variables – Previous Year Questions

11 GATE previous year questions on Complex variables (Engineering Mathematics, Instrumentation Engineering) with answers and explanations, from every paper.

1. GATE 2021 IN Q34 (1 mark, Numerical answer) – For f(z)=1/(z2+6z+9) in the complex plane, C f(z)\,dz around the circle centred at the origin with unit radius is .
2. GATE 2021 IN Q36 (2 marks, Multiple choice) – The series (z-1)-1-1+(z-1)-(z-1)2+ represents .
3. GATE 2022 IN Q50 (2 marks, Multiple select) – For z=(a+jb)/(a-jb) with a>0,b>0, which statements are true?
4. GATE 2022 IN Q61 (2 marks, Numerical answer) – For f(z)=1/[(z+1)(z+2)(z+3)], the residue at z=-1 is .
5. GATE 2023 IN Q19 (1 mark, Multiple choice) – Expanding F(z)=1/(1-z) around z=2 gives F(z)= k=0 a k(z-2)k, with ROC z-2 <1. For k0, the coefficients are
6. GATE 2023 IN Q39 (2 marks, Multiple choice) – Let f(z)=j(1-z)/(1+z), where z is complex and j=-1. Its inverse f-1 maps the real axis to the .
7. GATE 2024 IN Q11 (1 mark, Multiple choice) – Let z=x+iy be a complex variable and z its complex conjugate. The equation z2+z2=2 represents a
8. GATE 2024 IN Q49 (2 marks, Multiple select) – Both f(z)=u(x,y)+iv(x,y) and f(z)=u(x,y)-iv(x,y) are analytic in a domain. Choose all correct statements.
9. GATE 2025 IN Q33 (1 mark, Numerical answer) – For f(z)=2z+1z2-z, where z is complex, the sum of residues at its singular points is (in integer).
10. GATE 2025 IN Q49 (2 marks, Multiple select) – Choose the correct statements about Cauchy’s theorem for C f(z)\,dz, where C is a simple closed path in a simply connected domain D.
11. GATE 2026 IN Q13 (1 mark, Multiple choice) – Consider a function f(z)=z2+z+1, where zC is a complex variable. A simple closed contour in the z-plane encloses the point z=1+0j. The value of…