If |z-3+2 i| 4 then the difference between the greatest value and the least value of |z| is

Step-by-step solution

|z-(3-2 i)| 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 R S is the normal of the circle passing through origin ' O ' and G is its center (3,-2) Here, O R is the least distance and O S is the greatest distance O R=R G-O G and O S=O G+G S (1) As, R G=G S=4O G= 3^2+(-2)^2 = 9+4 = 13 From (1), O R=4- 13 and O S=4+ 13 So, required difference aligned &=(4+ 13 )-(4- 13 ) &= 13 + 13 =2 13 aligned