PYQ Vault
EbooksTutor

Determinant whose entries are powers of omega

This type of question, asked 2 times: 10 May 2023 S2, 11 May 2023 S2. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    10 May 2023 S2

    120
    If ω=−1−i32\omega = \frac{-1-i\sqrt{3}}{2} where i=−1i = \sqrt{-1}, then the value of ∣1ωω2ωω21ω21ω∣\begin{vmatrix}1&\omega&\omega^2\\\omega&\omega^2&1\\\omega^2&1&\omega\end{vmatrix} is

    Tap an option to check your answer.

  2. Question 2

    11 May 2023 S2

    143
    Let ω=−12+i32, i=−1\omega = -\frac{1}{2}+i\frac{\sqrt{3}}{2},\ i=\sqrt{-1}, then the value of ∣1111−1−ω2ω21ω2ω4∣\begin{vmatrix}1&1&1\\1&-1-\omega^2&\omega^2\\1&\omega^2&\omega^4\end{vmatrix} is

    Tap an option to check your answer.