TS EAMCET · Maths · Complex Number
If \((\sqrt{3}+i)^{10}=a+b i, a, b \in \mathbf{R}\), then the values of \(a\) and \(b\) are respectively
- A 64 and \(-64 \sqrt{3}\)
- B 128 and \(128 \sqrt{3}\)
- C 256 and \(256 \sqrt{3}\)
- D 512 and \(-512 \sqrt{3}\)
Answer & Solution
Correct Answer
(D) 512 and \(-512 \sqrt{3}\)
Step-by-step Solution
Detailed explanation
Let \(z=\sqrt{3}+i \Rightarrow|z|=\sqrt{3+1}=2\) and \(\arg (z)=\tan ^{-1} \frac{1}{\sqrt{3}}=\frac{\pi}{6}\) \(\therefore\) Polar form of \(z=2\left(\cos \frac{\pi}{6}+i \sin \frac{\pi}{6}\right)\)…
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