Choose the correct alternative: If ω ≠ 1 is a cubic root of unity and `|(1, 1, 1),(1, - omega^2 - 1, omega^2),(1, omega^2, omega^7)|` = 3k, then k is equal to

Choose the correct alternative: If ω ≠ 1 is a cubic root of unity and |1111-ω2-1ω21ω2ω7| = 3k, then k is equal to - Mathematics

Question

Choose the correct alternative:

If ω ≠ 1 is a cubic root of unity and $| \begin{matrix} 1 & 1 & 1 \\ 1 & - ω^{2} - 1 & ω^{2} \\ 1 & ω^{2} & ω^{7} \end{matrix} |$ = 3k, then k is equal to

Options

1
– 1
$\sqrt{3} i$
$- \sqrt{3} i$

MCQ

Solution

$- \sqrt{3} i$

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de Moivre’s Theorem and Its Applications

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Q 23 Q 22 Q 24

Chapter 2: Complex Numbers - Exercise 2.9 [Page 94]

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Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 12 TN Board

Chapter 2 Complex Numbers
Exercise 2.9 | Q 23 | Page 94

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Choose the correct alternative: If ω ≠ 1 is a cubic root of unity and |1111-ω2-1ω21ω2ω7| = 3k, then k is equal to - Mathematics

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