you should post the problem in its entirety.
you could solve for
, you would get it as a function of x and y and you minimize and maximize that. but that requires calc 3. so too much work.
another way is to let geometry help you. if you graphed what's happening in the complex plane, you would notice that z must lie on the circle of radius 2 centered at (3,3). draw a line from the origin passing through (3,3) cutting right across the circle. the length of the line segment from the origin to the first place the line cuts the circle is the min |z|, add the diameter of the circle to that, that is, add 4, and you get the max |z|
(by the way, | is a symbol found on your keyboard. hold down shift and press \)