TS EAMCET · Maths · Complex Number
If \(\left(\frac{\sqrt{3}+i}{\sqrt{3}-i}\right)^4+\left(\frac{\sqrt{3}-i}{\sqrt{3}+i}\right)^4=r\) cis \(\theta\), then one of the values of \(\sqrt{\mathrm{r} \operatorname{cis} \theta}\) is
- A \(\operatorname{cis}\left(\frac{3 \pi}{4}\right)\)
- B \(\operatorname{cis}\left(\frac{3 \pi}{2}\right)\)
- C \(\operatorname{cis}\left(\frac{\pi}{3}\right)\)
- D \(\operatorname{cis} \pi\)
Answer & Solution
Correct Answer
(B) \(\operatorname{cis}\left(\frac{3 \pi}{2}\right)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { }\left(\frac{\sqrt{3}+i}{\sqrt{3}-i}\right)^4+\left(\frac{\sqrt{3}-i}{\sqrt{3}+i}\right)^4 \\ & =\left(\frac{\sqrt{3}+i}{\sqrt{3}-i} \times \frac{\sqrt{3}+i}{\sqrt{3}+i}\right)^4+\left(\frac{\sqrt{3}-i}{\sqrt{3}+i} \times…
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