Question

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

• A. $\bar{a}z-a\bar{z}=0$
• B. $\bar{a}z+\bar{a}\bar{z}=0$
• C. $\bar{a}z+a\bar{z}=0$
• D. $\bar{a}z-\bar{a}\bar{z}=0$

Answer 1

Answer: (B)

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 ${}^{\prime }{-}^{\prime }y$-coordinate
$\therefore (\bar{a}+a)x-i(\bar{a}+a)y=0$
$\Rightarrow \bar{a}(x-iy)+a(x+iy)=0$
$\Rightarrow \bar{a}\bar{z}+az=0$