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If ω is a complex number such that 2ω + 1 = z where z = √−3. If | 1 1 1 ; 1 −ω^2 − 1 ω ; 1 ω^2 ω^7 | = 3k, then k is equal to :

1. 1
2. −z
3. z
4. −1

Correct answer: −z

Solution

The determinant of the given matrix can be calculated, and it simplifies to a value that is equal to -z, where z is defined as √−3. This shows that the correct option is -z, as it directly corresponds to the determinant's value.

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