The GATE Grind

GATE 2023 EC – Question 13

Engineering Mathematics · Complex Analysis · 1 mark · Multiple choice

Let $w^4=16j$. Which of the following cannot be a value of $w$?

  1. $2e^{j\frac{2\pi}{8}}$
  2. $2e^{j\frac{\pi}{8}}$
  3. $2e^{j\frac{5\pi}{8}}$
  4. $2e^{j\frac{9\pi}{8}}$

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Correct answer: (A) $2e^{j\frac{2\pi}{8}}$

Explanation

$16j=16e^{j\pi/2}$, so $w=2e^{j(\pi/2+2\pi k)/4}=2e^{j(\pi/8+k\pi/2)}$, i.e. angles $\pi/8,\ 5\pi/8,\ 9\pi/8,\ 13\pi/8$. The angle $2\pi/8$ is not in this list.