Complex Numbers And Quadratic Equations question 209
Question: The roots of $ {{(2-2i)}^{1/3}} $ are
Options:
A) $ \sqrt{2}( \cos \frac{\pi }{12}-i\sin \frac{\pi }{12} ),\sqrt{2}( -\sin \frac{\pi }{12}+i\cos \frac{\pi }{12} ),-1-i $
B) $ \sqrt{2}( \cos \frac{\pi }{12}+i\sin \frac{\pi }{12} ),\sqrt{2}( -\sin \frac{\pi }{12}-i\cos \frac{\pi }{12} ),1+i $
C) $ 1+\sqrt{2}i,-1-i,-2-2i $
D) None of the above
Show Answer
Answer:
Correct Answer: A
Solution:
Using De Moivre’s theorem $ {{(\cos \theta +i\sin \theta )}^{n}}=(\cos n\theta +i\sin n\theta ) $ and putting $ n=0 $ , 1, 2 then we get required roots.
BETA
