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  4. Reflection of the line baraz + a barz = 0 in the real axis is

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Q. Reflection of the line $ \bar{a}z + a\bar{z} = 0 $ in the real axis is

AMUAMU 2011Complex Numbers and Quadratic Equations

Solution:

Let $z = x + iy$
$\therefore \bar{a} ( x +iy) + a( x - iy) = 0$
$\Rightarrow (\bar{a} + a ) x + i(\bar{a} - a)y = 0$
For reflection of real axis, we take $'-' y$-coordinate
$\therefore (\bar{a} + a ) x - i (\bar{a} + a)y = 0$
$\Rightarrow \bar{a} ( x -iy) + a ( x + iy) = 0$
$\Rightarrow \bar{a}\bar{z} + az = 0$