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# Let $z=\begin{vmatrix}1&2+3i&4+5i\\2-3i&6&7+8i\\4-5i&7-8i&-9\end{vmatrix}$,then

$\begin{array}{1 1}(A)z \;is\;purely\;real \\ (B) z \;is\;purely\;imaginary \\ (C) z=0 \\(D) none\;of\;these \end{array}$

Can you answer this question?

Conjugate of z equals determinant obtained by taking conjugate of each of its element
$\overline {z}=\begin{vmatrix}1&2+3i&4+5i\\2-3i&6&7+8i\\4-5i&7-8i&-9\end{vmatrix}=z$
$\Rightarrow z$ is purely real.
Hence (A) is the correct answer.
answered Apr 9, 2014