Question

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

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

Answer 1

The correct option is A $x=3/5$

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

$=x-2ix+iy-2i^{2}y$

$x-2ix+iy+2y$

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

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

Comparing the values

$2x-y=1$

$x+2y=1$

on solving we get $x=\frac{3}{5},y=\frac{1}{5}$