Test center: the basic concept of complex number; Complex module. Special topic: computational problems; Change your mind. Analysis: Considering the geometric meaning of |Z+2-2i|= 1, it represents a circle with (-2,2) as the center and 1 as the radius, and the minimum value of |Z-2-2i| is the minimum value of the distance from the point on the circle to (2,2), which is converted into the center of the circle to.

Solution: Solution: |Z+2-2i|= 1 denotes a circle whose distance from a point on the complex plane to (-2,2) is 1.

|Z-2-2i| is the point on the circle, and the minimum distance to (2,2) is the center of the circle.

The distance to (2,2) minus the radius,

Namely: |2-(-2)|- 1=3.

So the answer is: 3

Comments: This question examines the basic concept of complex number, seeks the module of complex number, and examines the idea of transformation, which is the basic question.