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  4. If z = x+iy, then the equation |z+1| = |z-1| represents

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Q. If z = x+iy, then the equation |z+1| = |z-1| represents

KCETKCET 2020Complex Numbers and Quadratic Equations

Solution:

$|z+1|=|z-1|$
Let $z=x+i y$
Then, $|x+i y+1|=|x+i y-1|$
$\Rightarrow \sqrt{(x+1)^{2}+y^{2}}=\sqrt{(x-1)^{2}+y^{2}}$
$\Rightarrow (x+1)^{2}+y^{2}=(x-1)^{2}+y^{2}$
$\Rightarrow x^{2}+2 x+1+y^{2}=x^{2}+1-2 x+y^{2}$
$\Rightarrow 4 x=0$
$\Rightarrow x=0$ which represents $y-$ axis.