Complex Numbers
Properties of Complex Numbers
MMTS_Full_Test_15
Grade 12
Question:
If $z=x+iy$ and $|z-1|=|z+1|$, then
$x=0$
$y=0$
$x=y$
$x^2-y^2=1$
Step-by-Step Solution
Key Concept: $|z-1|=|z+1|\Rightarrow$ perpendicular bisector of $(-1,0)$ and $(1,0)$
$|x-1+iy|=|x+1+iy|\Rightarrow(x-1)^2=( x+1)^2\Rightarrow x=0$.
Correct Answer: 2