Cluster 2: Represent complex numbers and their operations on the complex plane.Archived

Students will be introduced to the midpoint and distance formulas, both on number lines and in a coordinate plane. Students should have some previous experience with both of these formulas. The lesson allows practice on basic distance and midpoint concepts and progresses through the application of the formulas on a complex plane. Students will draw connections between the basic real number skills and coordinates in the complex plane involving the skills they will acquire during this lesson.

Type: Lesson Plan

This problem is intended to reinforce the geometric interpretation of distance between complex numbers and midpoints as modulus of the difference and average respectively.

Type: Problem-Solving Task

This lesson is designed to develop students' understanding of complex numbers, iterations, and two variable functions by introducing Mandelbrot and Julia sets. This lesson provides links to discussions and activities related to the Mandelbrot set as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: Problem-Solving Task

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations.

Type: Video/Audio/Animation