A circle with center α and radius r can be expressed as |z − α| = r.
The perpendicular bisector of segment αβ is |z − α| = |z − β|.
Example ① What geometric figure is represented by |z − (1+2i)| = 3?
Solution:A circle with center 1+2i and radius 3
Solution:A circle with center 1+2i and radius 3
Key Points
- |z−α|=r ⇔ a circle with center α and radius r
- |z−α|=|z−β| ⇔ equidistant from two points ⇔ perpendicular bisector
Practice Problems
- What geometric figure is represented by |z| = |z − 4|?
Solution and Explanation
- Answer:The line x = 2 (the perpendicular bisector passing through the midpoint of 0 and 4)