Complex Numbers And Quadratic Equations question 274
Question: If $ \omega $ is an imaginary cube root of unity, then the value of $ \sin [ ({{\omega }^{10}}+{{\omega }^{23}})\pi -\frac{\pi }{4} ] $ is [IIT Screening 1994]
Options:
A) $ -\sqrt{3}/2 $
B) $ -1/\sqrt{2} $
C) $ 1/\sqrt{2} $
D) $ \sqrt{3}/2 $
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Answer:
Correct Answer: C
Solution:
Given, $ \sin [ ({{\omega }^{10}}+{{\omega }^{23}})\pi -\frac{\pi }{4} ]=\sin [ (\omega +{{\omega }^{2}})\pi -\frac{\pi }{4} ] $ $ =\sin ( -\pi -\frac{\pi }{4} )=-\sin ( \pi +\frac{\pi }{4} )=\sin \frac{\pi }{4}=\frac{1}{\sqrt{2}} $ .
BETA
