Complex Numbers And Quadratic Equations question 833
Question: The value of $ {{(-i)}^{1/3}} $ is [Roorkee 1995]
Options:
A) $ \frac{1+\sqrt{3}i}{2} $
B) $ \frac{1-\sqrt{3}i}{2} $
C) $ \frac{-\sqrt{3}-i}{2} $
D) $ \frac{\sqrt{3}-2i}{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
Since $ \frac{-\sqrt{3}-i}{2}=-( \cos \frac{\pi }{6}+i\sin \frac{\pi }{6} ) $
Þ $ {{( \frac{-\sqrt{3}-i}{2} )}^{3}}=-{{( \cos \frac{\pi }{6}+i\sin \frac{\pi }{6} )}^{3}}=-i $ and $ \frac{\sqrt{3}-i}{2}=\cos \frac{\pi }{6}-i\sin \frac{\pi }{6} $ and $ {{( \frac{\sqrt{3}-i}{2} )}^{3}}=\cos \frac{\pi }{2}-i\sin \frac{\pi }{2}=-i $ .
BETA
