∵|Z2+|Z2−1||2=|Z2−|Z2+1||2 ⇒(Z2+|Z2−1|)(Z2+|Z2−1|)=(Z2−|Z2+1|)(Z2−|Z2+1|) ⇒Z2(|Z2−1|+|Z2+1|)+Z2(|Z2−1|+|Z2+1|)=|Z2+1|2−|Z2−1|2 ⇒(Z2+Z2)(|Z2+1|+|Z2−1|)=2(Z2+Z2) ⇒ Either Z2+Z2=0 or |Z2+1|+|Z2−1|=2 So, Z2 lies on imaginary axis or on real axis within [−1,1] Also |Z1−3|=
1
2
⇒Z1 lies on the circle having center 3 and radius