Complex Numbers And Quadratic Equations question 271
Question: $ {{( \frac{-1+i\sqrt{3}}{2} )}^{20}}+{{( \frac{-1-i\sqrt{3}}{2} )}^{20}}= $
Options:
A) $ 20\sqrt{3}i $
B) 1
C) $ \frac{1}{2^{19}} $
D) $ -1 $
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Answer:
Correct Answer: D
Solution:
As $ \frac{-1+i\sqrt{3}}{2}=\omega $ and $ \frac{-1-i\sqrt{3}}{2}={{\omega }^{2}} $
$ \therefore {{(\omega )}^{20}}+{{({{\omega }^{2}})}^{20}}={{\omega }^{18}}.{{\omega }^{2}}+{{\omega }^{39}}.\omega ={{\omega }^{2}}+\omega =-1 $
BETA
