AP EAMCET · Maths · Complex Number
One of the \(15^{\text {th }}\) roots of -1 is
- A cis 0
- B \(\operatorname{cis} \frac{14 \pi}{15}\)
- C \(\operatorname{cis} \frac{13 \pi}{15}\)
- D \(\operatorname{cis} \frac{8 \pi}{15}\)
Answer & Solution
Correct Answer
(C) \(\operatorname{cis} \frac{13 \pi}{15}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {Since }(-1)^{1 / 15}=(-\cos 2 \pi+i \sin 2 \pi)^{1 / 15} \\ & =\left(-\cos \frac{2 \pi}{15}+i \sin \frac{2 \pi}{15}\right)=\cos \left(\frac{13 \pi}{15}\right)+i \sin \left(\frac{13 \pi}{15}\right) \\ & =\operatorname{cis}\left(\frac{13…
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