TS EAMCET · Maths · Complex Number
One of the values of \((\sqrt{3}-i)^{\frac{2}{5}}\) is
- A \(2^{\frac{2}{5}}(1-\sqrt{3} \mathrm{i})\)
- B \(2^{\frac{-3}{5}}(\sqrt{3}+\mathrm{i})\)
- C \(2^{\frac{2}{5}}(\sqrt{3}-\mathrm{i})\)
- D \(2^{\frac{-3}{5}}(1+\sqrt{3} i)\)
Answer & Solution
Correct Answer
(D) \(2^{\frac{-3}{5}}(1+\sqrt{3} i)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text Z=(\sqrt{3}-i)^{2 / 5} \\ & \Rightarrow Z=2^{\frac{1}{5}}(1-\sqrt{3} i)^{\frac{1}{5}} \\ & =2^{\frac{2}{5}}\left(\cos \left(\frac{3 \pi}{2}+\frac{\pi}{6}\right)+i \sin \left(\frac{3 \pi}{2}+\frac{\pi}{6}\right)\right)^{\frac{1}{5}} \\ &…
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