TS EAMCET · Maths · Complex Number
If \(\omega\) is a complex cube root of unity, then \(\cos \left[\left(\omega^{1234}+\omega^{2021}\right) \pi-\frac{\pi}{4}\right]\) is equal to
- A \(\frac{1}{\sqrt{2}}\)
- B \(\frac{1}{2}\)
- C \(\frac{\sqrt{3}}{2}\)
- D \(\frac{-1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(D) \(\frac{-1}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} &\cos \left[\left(\omega^{1234}+\omega^{2021}\right) \pi-\frac{\pi}{4}\right]=\cos \left[\left(\omega+\omega^2\right) \pi-\frac{\pi}{4}\right] \\ & =\cos \left[-\pi-\frac{\pi}{4}\right]=\cos \left(\pi-\frac{\pi}{4}\right)=-\cos…
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