Question

If $z=\left|\begin{array}{ccc}3+3i& 5-i& 7-3i\\ i& 2i& -3i\\ 3-2i& 5+i& 7+3i\end{array}\right|$, then

• A. z is purely real
• B. z is purely imaginary
• C. 0
• D. none of these

Answer 1

Answer: (D)

none of these

$z=$ $\left|\begin{array}{ccc}3+3i& 5-i& 7-3i\\ i& 2i& -3i\\ 3-2i& 5+i& 7+3i\end{array}\right|$

On finding $\left|z\right|$ ie determinant value

$=3(1+i)\left[2i\right(7+3i)+3i(5+i\left)\right]-(5-i)\left[i\right(7+3i)+3i(3-2i\left)\right]+(7-3i)\left[i\right(5+i)-2i(3-2i\left)\right]$

$=-3(3i+61)$

Hence $\left|z\right|$ is complex so option $\left(d\right)$ is correct