TS EAMCET · Maths · Complex Number
\((\sqrt{3}+i)^{10}+(\sqrt{3}-i)^{10}=\)
- A \(1024 \sqrt{3}\)
- B 1024
- C 2048
- D \(512 \sqrt{3}\)
Answer & Solution
Correct Answer
(B) 1024
Step-by-step Solution
Detailed explanation
\( \sqrt{3}+i = 2e^{i\frac{\pi}{6}} \) \( (\sqrt{3}+i)^{10} = (2e^{i\frac{\pi}{6}})^{10} = 2^{10}e^{i\frac{10\pi}{6}} = 1024e^{i\frac{5\pi}{3}} \) \( (\sqrt{3}-i)^{10} = (2e^{-i\frac{\pi}{6}})^{10} = 2^{10}e^{-i\frac{10\pi}{6}} = 1024e^{-i\frac{5\pi}{3}} \)…
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