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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 anticlo…

Q1

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

[JEE Main 2023, 11 Apr (Shift 1)]

a

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

b

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

c

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

d

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

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