The question asks for minimum/maximum distances, ranges of |z|, or bounds on expressions involving complex numbers constrained to lie on or within specified regions, circles, or intersections of loci.
Below, line segments $[ A B ]$ and $[ C D ]$ are given in the complex number plane. For each complex number z taken on these line segments, the number $\mathrm { w } = \mathrm { z } \cdot \overline { \mathrm { z } }$ is defined. Accordingly, in which of the following are the minimum and maximum values that w can take given respectively? A) 5 and 20 B) 5 and 25 C) 5 and 30 D) 10 and 20 E) 10 and 25