1. Tardigrade
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  3. Mathematics
  4. In the multiplicative group whose elements are the cube roots of unity, namely 1, ω, ω2 the inverse of the element ω is

Q. In the multiplicative group whose elements are the cube roots of unity, namely $\left\{1, \omega, \omega^{2}\right\}$, the inverse of the element $\omega$ is

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Solution:

$\theta=2 \tan ^{-1}\left(\frac{b}{a}\right)=2 \tan ^{-1}\left(\frac{3}{4}\right)$
$=\tan ^{-1}\left(\frac{2(3 / 4)}{1-9 / 16}\right)=\tan ^{-1}\left(\frac{3 / 2}{7 / 16}\right) $
$\therefore \theta=\tan ^{-1}\left(\frac{24}{7}\right)$

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