Question

If x,y,z are complex numbers, and Δ= beginvmatrix 0 & -y & -z
bary & 0 & -x
barz & barx & 0 endvmatrix, then Δ is:

• A. purely real
• B. purely imaginary
• C. complex
• D. 0

Hint:

Determinants with conjugate symmetry often yield purely real or imaginary values.

Answer 1

The Correct Option is B

Step 1: Observe that the determinant involves complex conjugate pairs.
Step 2: On expansion, Δ becomes the negative of its own conjugate.
Step 3: Hence Δ+Δ=0, implying Δ is purely imaginary.