The correct options are
A |z−2|=|z+2|
C |z−1−i|=|z+1−i|
Given : ω=(1−z)21−z2
⇒ω=1−z1+z=z¯¯¯z−zz¯¯¯z+z⇒ω=¯¯¯z−1¯¯¯z+1=−¯¯¯ω⇒ω+¯¯¯ω=0
So, ω should be purely imaginary
Hence, the locus of ω is x=0
Now, by obersvation, we see that all the options given represents perpendicular bisector.
|z−2|=|z+2|
Perpendicular bisector of points (2,0) and (−2,0)
Which is x=0
|z−2i|=|z+2i|
Perpendicular bisector of points (0,2) and (0,−2)
Which is y=0
|z−1−i|=|z+1−i|⇒|z−(1+i)|=|z−(−1+i)|
Perpendicular bisector of points (1,1) and (−1,1)
Which is x=0
|z−i|=|z+i|
Perpendicular bisector of points (0,1) and (0,−1)
Which is y=0