JEE Advanced Model Paper 15 with solutions for online practice

Method-l:Using Geometry

|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