Question

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

• A. A circle
• B. A parabola
• C. X-axis
• D. Y-axis

Answer 1

Answer: (D)

Y-axis

Answer 2

$|z+1|=|z-1|$
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.

so, The correct option is(D): Y-axis.