TS EAMCET · Maths · Complex Number
One of the values of \((\sqrt{3}-i)^{\frac{1}{6}}\) is
- A \(2^{\frac{1}{6}} \operatorname{cis} \frac{61 \pi}{36}\)
- B \(2^{\frac{1}{6}} \operatorname{cis} \frac{37 \pi}{36}\)
- C \(2^{\frac{1}{6}} \operatorname{cis} \frac{59 \pi}{36}\)
- D \(2^{\frac{1}{6}} \operatorname{cis} \frac{49 \pi}{36}\)
Answer & Solution
Correct Answer
(C) \(2^{\frac{1}{6}} \operatorname{cis} \frac{59 \pi}{36}\)
Step-by-step Solution
Detailed explanation
\(Z=(\sqrt{3}-i)^{1 / 6} \Rightarrow Z^6=(\sqrt{3}-i)\)…
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