AP EAMCET · Maths · Complex Number
If \((\sqrt{3}-\mathrm{i})^{\mathrm{n}}=2^{\mathrm{n}}, \mathrm{n} \in \mathrm{N}\), then the least possible value of n is
- A \(3\)
- B \(4\)
- C \(6\)
- D \(12\)
Answer & Solution
Correct Answer
(D) \(12\)
Step-by-step Solution
Detailed explanation
\(\sqrt{3}-\mathrm{i} = 2\left(\cos\left(-\frac{\pi}{6}\right) + \mathrm{i}\sin\left(-\frac{\pi}{6}\right)\right)\) \(\left[2\left(\cos\left(-\frac{\pi}{6}\right) + \mathrm{i}\sin\left(-\frac{\pi}{6}\right)\right)\right]^{\mathrm{n}} = 2^{\mathrm{n}}\)…
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