Question

If the conjugate of $\left(x+iy\right)\left(1-2i\right)$ is $1+i$, then

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

Answer 1

Answer: (A), (B)

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

Given,

$(x+iy)(1-2i)$

$=>x-2xi+iy+2y$

$=>(x+2y)+i(y-2x)$

Now,

Conjugate of this

$=(x+2y)-i(y-2x)$

Equating the coefficients of real and imaginary part from (1+i),

$x+2y=1------\left(1\right)$

$-(y-2x)=1----\left(2\right)$

solving 1 &2, we get,

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