JEE Mains · Maths · STD 11 - 4.1 complex nubers
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 \(...........\).
- A \(-\pi+\tan ^{-1} \frac{33}{5}\)
- B \(-\pi-\tan ^{-1} \frac{33}{5}\)
- C \(-\pi+\tan ^{-1} \frac{8}{9}\)
- D \(\pi-\tan ^{-1} \frac{8}{9}\)
Answer & Solution
Correct Answer
(D) \(\pi-\tan ^{-1} \frac{8}{9}\)
Step-by-step Solution
Detailed explanation
\(W _1= z _{ i } i =(5+4 i ) i =-4+5 i\) \(W _2= z _2(- i )=(3+5 i )(- i )=5-3 i\) \(W _1- W _2=-9+8 i\) \(\text { Principal argument }=\pi-\tan ^{-1}\left(\frac{8}{9}\right)\)
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