If z 1 = -1 + i and z 2 = 2i, where i = -1, then Arg(z 1/z 2) is

GATE 2024 CH – Question 13

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

If $z_1 = -1 + i$ and $z_2 = 2i$, where $i = \sqrt{-1}$, then $\text{Arg}(z_1/z_2)$ is

$\frac{3\pi}{4}$
$\frac{\pi}{4}$
$\frac{\pi}{2}$
$\frac{\pi}{3}$

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

Explanation

$\frac{z_1}{z_2} = \frac{-1 + i}{2i} = \frac{(-1 + i)(-i)}{2} = \frac{i + 1}{2}$, which has equal real and imaginary parts in the first quadrant, so its argument is $\frac{\pi}{4}$.