Question

If $(x+iy)(2-3i)=4+i$, then values of $x$ and $y$ are

• A. $x=\frac{5}{11},y=\frac{7}{11}$
• B. $x=\frac{5}{13},y=\frac{7}{13}$
• C. $x=\frac{5}{13},y=\frac{14}{13}$
• D. $x=\frac{5}{11},y=\frac{7}{13}$

Answer 1

The correct option is C $x=\frac{5}{13},y=\frac{14}{13}$

$(x+iy)(2-3i)=4+i$
$\Rightarrow (2x+3y)+i(2y-3x)=4+i$
Equating the real and imaginary parts separately, we get
$\Rightarrow 2x+3y=4\text{and}-3x+2y=1$

On solving both the above equations, we get
$x=\frac{5}{13}$ and $y=\frac{14}{13}$