If $z_1 = -1$ and $z_2 = i$, then find $\mathrm{Arg}\left(\dfrac{z_1}{z_2}\right)$.

If z₁ = -1 and z₂ = i, then find mathrmArg((z₁)/(z₂)).

Question 10 of 19

z_1 = -1

Yanam BieapBIEAP Intermediate Board 2023Subjective· 2mImportance★★★★★

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Simplify $z_1/z_2$ to a single complex number first, then read off its argument.

Given $z_1=-1$ , $z_2=i$ .

$\frac{z_1}{z_2} = \frac{-1}{i} = \frac{-1}{i}\cdot\frac{-i}{-i} = \frac{i}{-i^2} = \frac{i}{1} = i,$

using $i^2=-1$ . So $z_1/z_2 = i = 0 + 1\cdot i$ , which lies on the positive imaginary axis.

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