AP EAMCET · Maths · Complex Number
One of the complex roots of the equation \(x^{11}-x^6-x^5+1=0\) is
- A \(\operatorname{cis} \frac{3 \pi}{5}\)
- B \(\operatorname{cis} \frac{\pi}{3}\)
- C \(\operatorname{cis} \frac{5 \pi}{6}\)
- D cis \(\frac{7 \pi}{5}\)
Answer & Solution
Correct Answer
(B) \(\operatorname{cis} \frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \quad x^{11}-x^6-x^5+1=0 \\ & \Rightarrow \quad\left(x^6-1\right)\left(x^5-1\right)=0 \\ & \Rightarrow \quad x^6=1 \text { or } x^5=1 \\ & \Rightarrow \quad x=(1)^{\frac{1}{6}} \text { or } x=(1)^{\frac{1}{5}} \\ & x=\cos \frac{2 k \pi}{6}+i \sin \frac{2 k…
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