Search any question & find its solution
Question:
Answered & Verified by Expert
If $\alpha$ is a complex number such that $\alpha^{2}+\alpha+1=0$, then what is $\alpha^{31}$ equal to?
Options:
Solution:
2548 Upvotes
Verified Answer
The correct answer is:
$\alpha$
Since, $\alpha$ is a complex root therefore $\alpha^{2}+\alpha+1=0 \Rightarrow \alpha=\omega$ or $\omega^{2}$
consider $\alpha^{31}=(\omega)^{31}$
$=\left(\omega^{3}\right)^{10} \cdot \omega$
$=\omega \quad\left(\because \omega^{3}=1\right)$
$=\alpha$
consider $\alpha^{31}=(\omega)^{31}$
$=\left(\omega^{3}\right)^{10} \cdot \omega$
$=\omega \quad\left(\because \omega^{3}=1\right)$
$=\alpha$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.