Complex Numbers 1 Question 7
7.
If $\begin{vmatrix} 6 i & -3 i & 1 \\ 4 & 3 i & -1 \\ 20 & 3 & i \end{vmatrix}=x+i y$, then
(1998, 2M)
(a) $x=3, y=1$
(b) $x=1, y=1$
(c) $x=0, y=3$
(d) $x=0, y=0$
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Answer:
Correct Answer: 7. (d)
Solution:
- Given, $\begin{vmatrix}6 i & -3 i & 1 \\ 4 & 3 i & -1 \\ 20 & 3 & i\end{vmatrix}=x+i y$
$ \Rightarrow \quad -3i \begin{vmatrix} 6 i & 1 & 1 \\ 4 & -1 & -1 \\ 20 & i & i \end{vmatrix}=x+i y $
$ \Rightarrow \quad x+i y=0$
$\left[\because C _2 \text { and } C _3 \text { are identical }\right] $
$ \Rightarrow \quad x=0, y=0 $
