Curriculum placement
Precalculus. This describes the skill, not a learner estimate.
Distance and midpoints in the complex plane
Find complex-plane distances and midpoints using differences and averages
Problem types
- Distance and midpoint of complex numbers
Builds on
- The complex plane
- The conjugate of a complex number · Earlier idea
The squared modulus of a complex number is the number times its conjugate. The distance between z and w is the modulus of z − w, so its square is (z − w) times that difference's conjugate.
Leads to
- Conic sections and their equations · See it applied
The points z whose distance from w is a fixed number r form a circle, the first conic section.
Related skills
- Vectors and their components · Related idea
The distance between complex numbers is the length of the vector between their points.
- Dividing a segment in a given ratio · Related idea
The midpoint of two complex numbers is their average, the same as the midpoint of a segment.
- Solving absolute-value equations · Related idea
Absolute value is distance, and the modulus of a difference of two complex numbers is the distance between them in the plane.
Open the interactive map to explore lessons and skill connections.