Complex Numbers And Quadratic Equations question 659
Question: If $ \omega $ is imaginary cube root of unity, then $ \sin { ({{\omega }^{13}}+{{\omega }^{2}})\pi +\frac{\pi }{4} } $ is equal to
Options:
A) $ -\frac{\sqrt{3}}{2} $
B) $ -\frac{1}{\sqrt{2}} $
C) $ \frac{1}{\sqrt{2}} $
D) $ \frac{\sqrt{3}}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \sin { ( {{\omega }^{13}}+{{\omega }^{2}} )\pi +\frac{\pi }{4} } $ $ =\sin { ( \omega +{{\omega }^{2}} )\pi +\frac{\pi }{4} }=\sin ( -\pi +\frac{\pi }{4} ) $ $ =-sin\frac{\pi }{4}=-\frac{1}{\sqrt{2}} $
BETA
