# Maximum and minimum of complex numbers

For complex numbers z satisfying |z-8-16i| = 2sqrt(5), find the least possible value of |z| and the greatest possible value of |z|.

First I let z = x+iy and used this to write the equation in the form (x-8)^2 +(y-16)^2 = 20; then I solved for y and took the first derivative and set it equal to 0. I got the value of x as 8 and corresponding y values as 16+-2sqrt(5) then I used the second derivative test to determine the max and the min coordinate, then wrote them into Cartesian form as follows: 8+(16+-2sqrt(5))i = z and finally found |z|. However, the answer for the problem is max = 10sqrt(5) and min = 6sqrt(5). How??