Question

The equation $|z+1-i|=|z-1+i|$ represents a

• A. straight line
• B. circle
• C. parabola
• D. hyperbola

Answer 1

Answer: (A)

$|z+1-i|=|z-1+i|$
$\Rightarrow |z-(-1+i)|=|z-(1-i)|$
$\Rightarrow PA=PB$, where $A$ denotes the point $(-1,1),B$ denotes the point $(1,-1)$ and $P$ denotes the point $(x,y)$.
$\Rightarrow z$ lies on the perpendicular bisector of the line joining $A$ and $B$ and perpendicular bisector is a straight line.