AP EAMCET · Maths · Complex Number
If \(\omega\) is a complex cube root of unity, then
\(\sin \left[\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right]=\)
- A \(1 / \sqrt{2}\)
- B \(1 / 2\)
- C \(1\)
- D \(\sqrt{3} / 2\)
Answer & Solution
Correct Answer
(A) \(1 / \sqrt{2}\)
Step-by-step Solution
Detailed explanation
\(\sin \left[\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right]\) \(=\sin \left[\left(w+w^2\right) \pi-\frac{\pi}{4}\right] \quad\left(\because \omega^3=1\right)\)…
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