Search any question & find its solution
Question:
Answered & Verified by Expert
Let $\mathrm{O}$ be the origin and point $\mathrm{A}$ be represented byz. If OA is rotated through an angle $\pi / 2$ in the anticlockwise direction keeping the length of OA same, then what represents the new point?
Options:
Solution:
2510 Upvotes
Verified Answer
The correct answer is:
i
Let $z=\cos \theta+i \sin \theta$
Now, on rotating through an angle $\frac{\pi}{2}, z$ becomes
$\mathrm{Z}=\cos \left(\frac{\pi}{2}+\theta\right)+\mathrm{i} \sin \left(\frac{\pi}{2}+\theta\right)$
$=-\sin \theta+\mathrm{i} \cos \theta=\mathrm{i}^{2} \sin \theta+\mathrm{i} \cos \theta$
$=\mathrm{i}(\cos \theta+\mathrm{i} \sin \theta)=\mathrm{i} \mathrm{z}$
Now, on rotating through an angle $\frac{\pi}{2}, z$ becomes
$\mathrm{Z}=\cos \left(\frac{\pi}{2}+\theta\right)+\mathrm{i} \sin \left(\frac{\pi}{2}+\theta\right)$
$=-\sin \theta+\mathrm{i} \cos \theta=\mathrm{i}^{2} \sin \theta+\mathrm{i} \cos \theta$
$=\mathrm{i}(\cos \theta+\mathrm{i} \sin \theta)=\mathrm{i} \mathrm{z}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.