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  • Let w1 be the point obtained by the rotation of z1 = 5 + 4i about the origin through a right angle in the anticlockwise direction, and w2 be the point obtained by the rotation of z2 = 3 + 5i

Let w1 be the point obtained by the rotation of z1 = 5 + 4i about the origin through a right angle in the
anticlockwise direction, and w2 be the point obtained by the rotation of z2 = 3 + 5i about the origin through a
right angle in the clockwise direction. Then the principal argument of w1 – w2 is equal to :

Option: 1

\pi-\tan ^{-1} \frac{8}{9}


Option: 2

-\pi+\tan ^{-1} \frac{8}{9}


Option: 3

\pi-\tan ^{-1} \frac{33}{5}


Option: 4

-\pi+\tan ^{-1} \frac{33}{5}


Answers (1)

\begin{aligned} & \mathrm{W}_1=\mathrm{z}_{\mathrm{i}} \mathrm{i}=(5+4 \mathrm{i}) \mathrm{i}=-4+5 \mathrm{i} \ldots \text { (i) } \\ & \mathrm{W}_1=\mathrm{z}_2(-\mathrm{i})=(3+5 \mathrm{i})(-\mathrm{i})=5-3 \mathrm{i} \ldots \\ & \mathrm{W}_1-\mathrm{W}_2=-9+8 \mathrm{i} \\ & \text { Principal argument }=\pi-\tan ^{-1}\left(\frac{8}{9}\right) \end{aligned}

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Kshitij

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