Let $w_{1}$ be the point obtained by the rotation of $z_{1}=5+4 i$ about the origin through a right angle in the anticlockwise direction, and $w_{2}$ be the point obtained by the rotation of $z_{2}=3+5 i$ about the origin through a right angle in the clockwise direction. Then the principal argument of $w_{1}-w_{2}$ is equal to :

Question

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

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

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

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

Solution

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