Question

The reflection of the complex number $\frac{4+3i}{1+2i}$ in the straight line $iz=\overline{z},$ is

• A. $2+i$
• B. $2-i$
• C. $1+2i$
• D. $1-2i$

Answer 1

The correct option is D $1-2i$

We have, $z_1=\frac{4+3i}{1+2i}=\frac{(4+3i)(1-2i)}{(1+2i)(1-2i)}=\frac{10-5i}{5}=2-i$

which represents the point whose coordinates are $(2,-1)$

Also, we have,

$iz=\overline{z}\Rightarrow i(x+iy)-(x-iy)=0$ $($ putting $z=x+iy)$

$\Rightarrow i(x+y)-(x+y)=0\Rightarrow (i-1)(x+y)=0$

which represents the line $y=-x$

Hence, reflection of the point $(2,-1)$ in the line $y=-x$ gives the point $(1,-2)$ which is equivalent to $1-2i$ in the argand plane.