Let $\omega$ be a complex number such that $2 \omega+1=z$, when $z=\sqrt{-3}$ if $\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & -\omega^2-1 & \omega^2 \\ 1 & \omega^2 & \omega^7\end{array}\right|=3 k$, then $k$ is equal to

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Analyzing +4 | -1

Let

\omega

be a complex number such that

2 \omega+1=z

, when

z=\sqrt{-3}

\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & -\omega^2-1 & \omega^2 \\ 1 & \omega^2 & \omega^7\end{array}\right|=3 k

, then

k

is equal to

View answer and explanation

Correct option: B

-z

Option B (-z) is correct because simplifying the determinant using properties of

\omega

leads to

k = -z

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