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Q.
The reflection of the complex number $\frac{4+3 i}{1+2 i}$ in the straight line $i z=$ is
Complex Numbers and Quadratic Equations
Solution:
We have,
$ z_{1} =\frac{4+3 i}{1+2 i}=\frac{(4+3 i)(1-2 i)}{(1+2 i)(1-2 i)} $
$=\frac{10-5 i}{5}=2-i $
which represents the point whose coordinates are $(2, -1)$
Also, we have,
$i z=\bar{z}$
$\Rightarrow i(x+i y)-(x-i y)=0$
$[$ Putting $z=x+i y]$
$\Rightarrow i(x+y)-(x+y)=0$
$\Rightarrow (i-1)(x+y)=0$
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 $1-2 i$ in the argand plane,