Find the real values of $x$ and $y$ for which the following equation is satisfied : $\frac{(1+i) x-2

Question

Find the real values of $x$ and $y$ for which the following equation is satisfied : $\frac{(1+i) x-2 i}{3+i}+\frac{(2-3 i) y+i}{3-i}=i$

Professor PC Thomas Classes · Answer

$\frac{(1+i) x-2 i}{3+i}+\frac{(2-3 i) y+i}{3-i}=i$\ $\Rightarrow(1+i)(3-i) x-2 i(3-i)+(2-3 i)(3+i)$ $y+i(3+i)=10 i$\ $\Rightarrow 4 x+2 i x-6 i-2+9 y-7 i y+3 i-1=10 i$\ $\Rightarrow \quad 4 x+9 y-3=0$ and $2 x-7 y-3=10$\ On solving, we get $x=3, y=-1$\