The GATE Grind

GATE 2025 AE – Question 16

Engineering Mathematics · Special topics: Fourier series, complex numbers, analytic functions and Cauchy-Riemann equations · 1 mark · Multiple choice

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

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

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Correct answer: (A) 2

Explanation

$(1 + i)^2 = 2i$, so $(1 + i)^3 = 2i(1 + i) = -2 + 2i = 2(i - 1)$. Dividing by $(i - 1)$ gives 2.