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 \(\frac{1}{\sqrt{2}}\)
- B \(\frac{1}{2}\)
- C 1
- D \(\frac{\sqrt{3}}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
It is given that \(w\) is a complex cube root of unity, so \(w^3=1\) and \(w^2+w+1=0\). So, \(\sin \left\{\left(w^{10}+w^{23}\right) \pi-\frac{\pi}{4}\right\}\)…
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