|Z1−1| = 1 ⇒ z1 lies on a circle with centre 1 +0i and radius unity |Z2+4| = 2 ⇒ z2 lies on a circle with centre-4+0i and radius2 units |z1−z2| represents the distance between z1 and z2 ∴ Max. value of |z1−z2| = Max. distance between two any two points on the two given circles [lies along their common normal. Hence, Max. value of |z1−z2| is AC = CO + OA = 8 Min value is clearly 2