Question

If x, y, z are complex numbers, then $△$ =$\left|\begin{array}{ccc}0& -y& -z\\ \overline{y}& 0& -x\\ \overline{z}& \overline{x}& 0\end{array}\right|$ is equal

• A. Purely real
• B. Purely imaginary
• C. Complex
• D. 0

Answer 1

Answer: (B)

Purely imaginary

$△$= $
\left |
\begin{array}{111}
0 & -\overline{y} & -\overline{z} \\
y & 0 & -\overline{x} \\
z & x & 0 \\
\end {array}
\right |
$
Now change rows into columns and columns into rows and take (-1) common from each row
$\therefore \overline{△}=(-1{)}^3△=-△\therefore △+△=0$
$\Rightarrow$2(real part)=0
$\therefore △$ is purely imaginary.