[JEE Advanced 1998] if omega is an imaginary cube root of unity then 1 omega omega 2
If $\omega$ is an imaginary cube root of unity, then $(1+\omega-\omega^2)^7$ equals
(a) $128\omega$
(b) $-128\omega$
(c) $128\omega^2$
(d) $-128\omega^2$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (d) $-128\omega^2$
$1+\omega=-\omega^2$, so $1+\omega-\omega^2=-2\omega^2$; $(-2\omega^2)^7=-128\,\omega^{14}=-128\omega^2$.
JEE Advanced 1998 · Complex Numbers — verified solution by the Vidaara Team.
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