jee-main 2017 Q62

jee-main · India · 02apr Complex Numbers Arithmetic Roots of Unity and Cyclotomic Expressions

Let $\omega$ be a complex number such that $2\omega + 1 = z$ where $z = \sqrt{-3}$. If
$$\begin{vmatrix} 1 & 1 & 1 \\ 1 & -\omega^2 - 1 & \omega^2 \\ 1 & \omega^2 & \omega^7 \end{vmatrix} = 3k$$
Then $k$ can be equal to:
(1) $-z$
(2) $\frac{1}{z}$
(3) $-1$
(4) $1$

Let $\omega$ be a complex number such that $2\omega + 1 = z$ where $z = \sqrt{-3}$. If

$$\begin{vmatrix} 1 & 1 & 1 \\ 1 & -\omega^2 - 1 & \omega^2 \\ 1 & \omega^2 & \omega^7 \end{vmatrix} = 3k$$

Then $k$ can be equal to:\\
(1) $-z$\\
(2) $\frac{1}{z}$\\
(3) $-1$\\
(4) $1$

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