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GATE 2025 CH – Question 13

Engineering Mathematics · Complex Variables: Complex numbers and polar form · 1 mark · Multiple choice

Consider two complex numbers $z_1 = 1 - i$ and $z_2 = i$. The argument of $z_1 z_2$ is

  1. 0
  2. $\frac{\pi}{4}$
  3. $\frac{\pi}{2}$
  4. $\pi$

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Show answer and explanation

Correct answer: (B) $\frac{\pi}{4}$

Explanation

The product is $z_1z_2 = (1 - i)i = i - i^2 = 1 + i$, which lies in the first quadrant with equal real and imaginary parts, so its argument is $\tan^{-1}(1) = \frac{\pi}{4}$.