Complex Numbers And Quadratic Equations question 383
Question: If $ z=\sqrt{2}-i\sqrt{2} $ is rotated through an angle $ 45{}^\circ $ in the anti-clockwise direction about the origin, then the coordinates of its new position are [Kerala (Engg.) 2005]
Options:
A) (2, 0)
B) ( $ \sqrt{2},\sqrt{2} $ )
C) $ (\sqrt{2},-\sqrt{2} $ )
D) $ (\sqrt{2},0) $
E) (4, 0)
Show Answer
Answer:
Correct Answer: D
Solution:
$ z=\sqrt{2}-i\sqrt{2} $ Here, $ \theta ={{\tan }^{-1}}( \frac{-\sqrt{2}}{\sqrt{2}} ) $ = $ {{\tan }^{-1}}(-1) $ = $ 135^{o} $ Now, rotate z in opposite direction with 45° angle
$ \therefore $ $ \theta =180{}^\circ $
$ \therefore $ $ \theta ={{\tan }^{-1}}(0)={{\tan }^{-1}}( \frac{0}{\sqrt{2}} ) $
Þ Hence $ x=\sqrt{2} $ and $ y=0 $ .
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