Q47 / 160 · TS EAMCET 2022 (20 Jul Shift 2) · Mathematics
If $\left|\begin{array}{cc}2+3 i & i \\ 1-2 i & -i\end{array}\right|=x+i y$, then $x+y=$
- Correct answerA-2
- B-4
- C-8
- D4
Solution
$$
\begin{aligned}
& \text { }\left[\begin{array}{cc}
2+3 \mathrm{i} & \mathrm{i} \\
1-2 \mathrm{i} & -\mathrm{i}
\end{array}\right]=\mathrm{x}+\mathrm{iy} \\
& \Rightarrow(2+3 \mathrm{i})(-\mathrm{i})-\mathrm{i}(1-2 \mathrm{i})=\mathrm{x}+\mathrm{iy} \\
& \Rightarrow-2 \mathrm{i}+3-\mathrm{i}-2=\mathrm{x}+\mathrm{iy} \\
& \Rightarrow 1-3 \mathrm{i}=\mathrm{x}+\mathrm{iy} \\
& \Rightarrow \mathrm{x}=1 \quad \& \quad \mathrm{y}=-3 \\
& \therefore \mathrm{x}+\mathrm{y}=1-3=-2
\end{aligned}
$$
Hence, the correct answer is option: 'A'.