Let z=x+iy ∴|z−1|=|z−2|=|z−i| ⇒|(x−1)+iy|=|(x−2)+iy| =|(x+i(y−1)| ⇒x2−2x+1+y2=x2+4−4x+y2 =x2+y2+1−2y Taking Ist and IInd term ⇒ −2x+1=4−4x ⇒ 2x=3 ......(i) Taking IInd and IIIrd term ⇒4−4x=1−2y ⇒ 4x−2y=3 .............(ii) Taking Ist and IIIrd term −2x+1=1−2y ⇒2x−2y=0 ⇒x=y ..........(iii) From (i) x=
3
2
On putting value of x in Eq. (iii), we get y=
3
2
On putting the value of x and y in Eq. (ii), we get 4(