Official solution
\[\left| {z - \left( {3 - 2i} \right)} \right| \le 4\] represents a circle whose center is (3, -2) and radius = 4.
\[\left| z \right|\] = \[\left| z -0\right|\] 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 in the greatest distance
OR = RG - OG and OS = OG + GS . . . . .(1)
As, RG = GS = 4
OG = \[\sqrt {{3^2} + \left( { - 2{)^2}} \right)} \] = \[\sqrt {9 + 4} \] = \[\sqrt {13} \]
From (1), OR = 4 - \[\sqrt {13} \] and OS = 4 + \[\sqrt {13} \]
So, required difference = \[\left( {4 + \sqrt {13} } \right)\] - \[\left( {4 - \sqrt {13} } \right)\]
= \[\sqrt {13} + \sqrt {13} \] = \[2\sqrt {13} \]