GATE AE Complex Analysis & Fourier Series: Previous Year Questions

GATE AE (Aerospace Engineering) Complex Analysis & Fourier Series previous year questions from the Engineering Mathematics section, with figures and the official answer key where available.

All GATE AE papers

GATE AE 2026, Question 12 (1 mark, MCQ)

Engineering Mathematics - Complex Analysis & Fourier Series

The Fourier series representation of a square wave is shown in the figure below. The fluctuations seen near $x = \pm 1$ are named after which one of the following scientists?

GATE AE 2026 question 12

  1. Cauchy
  2. Fourier
  3. Gibbs
  4. Laplace

Official answer: C

GATE AE 2025, Question 16 (1 mark, MCQ)

Engineering Mathematics - Complex Analysis & Fourier Series

If $i = \sqrt{-1}$, $\dfrac{(i+1)^3}{i-1} =$ _______.

  1. 2
  2. $-2$
  3. $(i+1)$
  4. $(i-1)$

Official answer: A

GATE AE 2022, Question 13 (1 mark, MCQ)

Engineering Mathematics - Complex Analysis & Fourier Series

Let $x$ be a real number and $i = \sqrt{-1}$. Then the real part of $\cos(ix)$ is

  1. $\sinh x$
  2. $\cosh x$
  3. $\cos x$
  4. $\sin x$

Official answer: B

GATE AE 2014, Question 12 (1 mark, MCQ)

Engineering Mathematics - Complex Analysis & Fourier Series

The series $s = \sum_{m=1}^{\infty} \dfrac{m^2}{3^m}(x-2)^m$ converges for all $x$ with $|x-2| \le R$ given by

  1. $R = 0$
  2. $R = 3$
  3. $R = \infty$
  4. $R = 1/3$

Official answer: B

GATE AE 2014, Question 37 (2 marks, MCQ)

Engineering Mathematics - Complex Analysis & Fourier Series

For the periodic function given by $f(x) = \begin{cases} -2, & -\pi < x < 0 \\ 2, & 0 < x < \pi \end{cases}$ with $f(x + 2\pi) = f(x)$, using Fourier series, the sum $s = 1 - \dfrac{1}{3} + \dfrac{1}{5} - \dfrac{1}{7} + \cdots$ converges to

  1. 1
  2. $\dfrac{\pi}{3}$
  3. $\dfrac{\pi}{4}$
  4. $\dfrac{\pi}{5}$

Official answer: C