Complex Numbers And Quadratic Equations question 831
Question: If $ -1+\sqrt{-3}=r{e^{i\theta }}, $ then $ \theta $ is equal to [RPET 1989; MP PET 1999]
Options:
A) $ \frac{\pi }{3} $
B) $ -\frac{\pi }{3} $
C) $ \frac{2\pi }{3} $
D) $ -\frac{2\pi }{3} $
Show Answer
Answer:
Correct Answer: C
Solution:
Here $ -1+\sqrt{-3}=r{e^{i\theta }} $ Þ $ -1+i\sqrt{3}=r{e^{i\theta }} $ $ =r\cos \theta +ir\sin \theta $ Equating real and imaginary parts, we get $ r\cos \theta =-1 $ and $ r\sin \theta =\sqrt{3} $ Hence $ \tan \theta =-\sqrt{3}\Rightarrow \tan \theta =\tan \frac{2\pi }{3} $ .Hence $ \theta =\frac{2\pi }{3} $ .
BETA
