TS EAMCET · Maths · Complex Number
The product of all the values of \((\sqrt{3}-i)^{\frac{3}{7}}\) is
- A \(8\)
- B \(-8\)
- C \(8i\)
- D \(-8i\)
Answer & Solution
Correct Answer
(D) \(-8i\)
Step-by-step Solution
Detailed explanation
\( \sqrt{3}-i = 2 \left(\cos\left(-\frac{\pi}{6}\right) + i\sin\left(-\frac{\pi}{6}\right)\right) \) Product \( = (\sqrt{3}-i)^3 = \left(2 \left(\cos\left(-\frac{\pi}{6}\right) + i\sin\left(-\frac{\pi}{6}\right)\right)\right)^3 \)…
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