TS EAMCET · Maths · Complex Number
\(\operatorname{Arg}\left(\sin \frac{6 \pi}{5}+i\left(1+\cos \frac{6 \pi}{5}\right)\right)=\)
- A \(\frac{5 \pi}{6}\)
- B \(\frac{6 \pi}{5}\)
- C \(\frac{2 \pi}{5}\)
- D \(\frac{9 \pi}{10}\)
Answer & Solution
Correct Answer
(D) \(\frac{9 \pi}{10}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \operatorname{Arg}\left(\sin \frac{6 \pi}{5}+i\left(1+\cos \frac{6 \pi}{5}\right)\right) \\ = & \operatorname{Arg}\left(2 \sin \frac{3 \pi}{5} \cdot \cos \frac{3 \pi}{5}+i \cdot 2 \cos ^2 \frac{3 \pi}{5}\right) \\ = & \operatorname{Arg}\left[\left(2 \cos…
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