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Let x, y and z be complex numbers. If \(\Delta\) denotes the determinant of the matrix \[ \begin{vmatrix} 0 & -y & -z \\ y & 0 & -x \\ z & x & 0 \end{vmatrix}, \] then \(\Delta\) is

1. purely real
2. purely imaginary
3. complex
4. zero

Correct answer: complex

Solution

The determinant of the given matrix involves complex numbers and results in a value that can have both real and imaginary components, making it a complex number. Therefore, the correct option is that B4 is complex.

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