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If the conjugate of $(x+i y)(1-2 i)$ is $1+i$, then
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Verified Answer
The correct answer is:
$x+i y=\frac{1-i}{1-2 i}$
We have, $\overline{(x+i y)(1-2 i)}=1+i$
$\Rightarrow \quad \overline{(x+i y)(1-2 i)}=1+i$
$\Rightarrow \quad(x-i y)(1+2 i)=1+i$
$\Rightarrow \quad x-i y=\frac{1+i}{1+2 i}$
$\Rightarrow \quad \overline{x-i y}=\overline{\left(\frac{1+i}{1+2 i}\right)}=\frac{1-i}{1-2 i}$
$\Rightarrow \quad x+i y=\frac{1-i}{1-2 i}$
$\Rightarrow \quad \overline{(x+i y)(1-2 i)}=1+i$
$\Rightarrow \quad(x-i y)(1+2 i)=1+i$
$\Rightarrow \quad x-i y=\frac{1+i}{1+2 i}$
$\Rightarrow \quad \overline{x-i y}=\overline{\left(\frac{1+i}{1+2 i}\right)}=\frac{1-i}{1-2 i}$
$\Rightarrow \quad x+i y=\frac{1-i}{1-2 i}$
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