If omega is complex cube root of unity, then the value of (1)/(omega) - omega is

March 24, 2026Mathematics

ScanSolve AI Answer

March 24, 2026

Answer

(1)(-\omega) - (\omega)(\omega) $$

Here are the solutions to the given problems:

*a) If $\omega$ is a complex cube root of unity, then the value of $\begin{vmatrix} 1 & \omega \\ \omega & -\omega \end{vmatrix}$ is

Step 1: Evaluate the determinant. The determinant of a $2 \times 2$ matrix $\begin{vmatrix} a & b \\ c & d \end{vmatrix}$ is $ad - bc$ . For the given matrix: $\begin{vmatrix} 1 & \omega \\ \omega & -\omega \end{vmatrix} = (1)(-\omega) - (\omega)(\omega)$ $= -\omega - \omega^2$

Step 2:

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Quick Answer

*a) If is a complex cube root of unity, then the value of 1 & \\ & - is Step 1: Evaluate the determinant.

Asked on March 24, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 24, 2026

Here are the solutions to the given problems: *a) If is a complex cube root of unity, then the value of 1 & \\ & - is Step 1: Evaluate the determinant. The determinant of a 2 × 2 matrix a & b \\ c & d is ad - bc. For the given matrix: 1 & \\ & - = (1)(-) - ()() = - - ^2 Step 2: