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

This cluster includes the following benchmarks.

Visit the specific benchmark webpage to find related instructional resources.

  • MAFS.912.N-CN.2.4 : Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
  • MAFS.912.N-CN.2.5 : Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (–1 + √3 i)³ = 8 because (–1 + √3 i) has modulus 2 and argument 120°.
  • MAFS.912.N-CN.2.6 : Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
Cluster Information
Number:
MAFS.912.N-CN.2
Title:
Represent complex numbers and their operations on the complex plane.
Type:
Cluster
Subject:
Mathematics - Archived
Grade:
912
Domain-Subdomain
Number & Quantity: The Complex Number System
Cluster Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Problem-Solving Tasks
  • Complex Distance: This problem is intended to reinforce the geometric interpretation of distance between complex numbers and midpoints as modulus of the difference and average respectively.

  • The Mandelbrot Set: 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.
Video/Audio/Animation
  • MIT BLOSSOMS - Fabulous Fractals and Difference Equations : 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.