|z−(3−2i)|≤4 represents a circle whose centre is (3,-2) and radius =4 |z|=|z−0| represents the distance of point z ' from origin (0,0)
Suppose RS is the normal of the circle passing through origin ' O ' and G is its center (3,-2) . Here, OR is the least distance and OS is the greatest distance OR=RG−OG and OS=OG+GS As, RG=GS=4 OG=√32+(−2)2=√9+4=√13 From (i), OR=4−√13 and OS=4+√13 So, required difference =(4+√13)−(4−√13) =√13+√13=2√13