Question

If the conjugate of $(x+iy)(1-2i)$ be $1+i,$ then:

• A. $x=\frac{3}{5}$
• B. $y=\frac{1}{5}$
• C. $x+iy=\frac{1-i}{1-2i}$
• D. $x-iy=\frac{1-i}{1+2i}$

Answer 1

Answer: (A), (B)

$x=\frac{3}{5}$
$y=\frac{1}{5}$

Conjugate of $(x+iy)(1-2i)$ is equal to $(x-iy)(1+2i)$

$\Rightarrow (x-iy)(1+2i)=1+i$

$\Rightarrow x-iy=\frac{1+i}{1+2i}$

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

$\Rightarrow x-iy=\frac{3-i}{5}$

Comparing real and imaginary parts ;

$\Rightarrow x=\frac{3}{5},y=\frac{1}{5}$