Question

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

• A. $1$, $3/13$
• B. $2$ , $5/13$
• C. $\frac{5}{13}$ , $\frac{14}{13}$
• D. $0$ , $2$

Answer 1

Answer: (C)

$\frac{5}{13}$ , $\frac{14}{13}$

Answer 2

$\left(x+iy\right)\left(2-3i\right)=4+i$ $\Rightarrow\, 2x+3y+i\left(-3x+2y\right)=4+i$ Equating real and imaginary parts, we get $2x+3y=4$ , $-3x+2y=1$ Solving these, we get $x=\frac{5}{13}$ , $y=\frac{14}{13}$