TS EAMCET · Maths · Complex Number
\({x \in[0,2 \pi]}\), \(\sin x+i \cos 2 x\) and \(\cos x-i \sin 2 x\) are conjugate to each other =
- A \(\left\{\frac{\pi}{4}, \frac{\pi}{2}, \frac{3 \pi}{4}, \pi, \frac{5 \pi}{4}, \frac{3 \pi}{2}, \frac{7 \pi}{4}, 2 \pi\right\}\)
- B \(\left\{\frac{\pi}{4}, \frac{3 \pi}{4}, \frac{5 \pi}{4}, \frac{7 \pi}{4}\right\}\)
- C \(\left\{\frac{\pi}{2}, \pi, \frac{3 \pi}{2}, 2 \pi\right\}\)
- D \(\phi\)
Answer & Solution
Correct Answer
(D) \(\phi\)
Step-by-step Solution
Detailed explanation
\(\sin x+i \cos 2 x = \overline{\left(\cos x-i \sin 2 x\right)}\) \(\sin x+i \cos 2 x = \cos x+i \sin 2 x\) \(\sin x = \cos x \implies \tan x = 1 \implies x = \frac{\pi}{4}, \frac{5\pi}{4}\)…
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