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Q.
If $(x+iy) (2-3i)=4+i$, then values of $x$, $y$ are
Complex Numbers and Quadratic Equations
Solution:
$\left(x+iy\right)\left(2-3i\right)=4+i$
$\Rightarrow \, 2x+3y+i\left(-3x+2y\right)=4+i$
Equating real and imaginary parts, we get
$2x+3y=4$ ,
$-3x+2y=1$
Solving these, we get $x=\frac{5}{13}$ ,
$y=\frac{14}{13}$