JEE Mains · Maths · STD 11 - 4.1 complex nubers
The complex number \(z=\frac{i-1}{\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}}\) is equal to \(.....\)
- A \(\sqrt{2}\left(\cos \frac{5 \pi}{12}+ i \sin \frac{5 \pi}{12}\right)\)
- B \(\cos \frac{\pi}{12}- i \sin \frac{\pi}{12}\)
- C \(\sqrt{2}\left(\cos \frac{\pi}{12}+ i \sin \frac{\pi}{12}\right)\)
- D \(\sqrt{2} i \left(\cos \frac{5 \pi}{12}- i \sin \frac{5 \pi}{12}\right)\)
Answer & Solution
Correct Answer
(A) \(\sqrt{2}\left(\cos \frac{5 \pi}{12}+ i \sin \frac{5 \pi}{12}\right)\)
Step-by-step Solution
Detailed explanation
\(Z =\frac{ i -1}{\cos \frac{\pi}{3}+ i \sin \frac{\pi}{3}}=\frac{ i -1}{\frac{1}{2}+\frac{\sqrt{3}}{2} i }\)…
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