# If conjugate of $(x+iy)(1-2i)=1+i$, then $(x,y)=?$

$\begin{array}{1 1}(A) (\large\frac{1}{5},\frac{1}{5}) \\(B) (-\large\frac{1}{5},\frac{1}{5}) \\(C) (\large\frac{1}{5},-\frac{1}{5}) \\ (D) (\large-\frac{1}{5},-\frac{1}{5}) \end{array}$

Given: $\overline {(x+iy)(1-2i)}=1+i$
$\Rightarrow\:(x+iy)(1-2i)=1-i$
$\Rightarrow\:x+iy=\large\frac{1-i}{1-2i}=\frac{-1+i}{5}$