Complex Numbers And Quadratic Equations question 118
Question: Argument of $ -1-i\sqrt{3} $ is [RPET 2003]
Options:
A) $ \frac{2\pi }{3} $
B) $ \frac{\pi }{3} $
C) $ -\frac{\pi }{3} $
D) $ -\frac{2\pi }{3} $
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Answer:
Correct Answer: D
Solution:
Let $ z=-1-i\sqrt{3} $ then $ \alpha ={{\tan }^{-1}}| \frac{b}{a} |={{\tan }^{-1}}| -\frac{\sqrt{3}}{1} |=\frac{\pi }{3} $ Clearly, z is in III quadrant. Therefore argument $ \theta =-(\pi -\alpha )=-(\pi -\pi /3)=\frac{-2\pi }{3} $ .
BETA
