If $(3 x+2)-(5 y-3) \mathrm{i}$ and $(6 x+3)+(2 y-4) \mathrm{i}$ are conjugates of each other, then the…
If $(3 x+2)-(5 y-3) \mathrm{i}$ and $(6 x+3)+(2 y-4) \mathrm{i}$ are conjugates of each other, then the value of $\frac{x-y}{x+y}$ is (where $\mathrm{i}=\sqrt{-1}, x, y \in \mathrm{R}$ )
$-1$
0
1
2
Solution
$(3 x+2)-(5 y-3) \mathrm{i}$ and $(6 x+3)+(2 y-4) \mathrm{i}$ are conjugates of each other.
$\Rightarrow 3 x+2=6 x+3$ and $5 y-3=2 y-4$
$\Rightarrow 3 x=-1$ and $3 y=-1$
$\Rightarrow x=-\frac{1}{3}$ and $y=-\frac{1}{3}$
$\therefore \quad \frac{x-y}{x+y}=0$