- MAFS.912.N-CN.1.1: Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.
- MAFS.912.N-CN.1.2: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
- MAFS.912.N-CN.1.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
|
Generated on 5/19/2026 at 6:59 AM |
The webpage this document was printed/exported from can be found at the following URL:
https://www.cpalms.org//PreviewIdea/Preview/1510
https://www.cpalms.org//PreviewIdea/Preview/1510
Standard 1: Perform arithmetic operations with complex numbers. (Algebra 2 - Additional Cluster) Archived
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Cluster Standards
This cluster includes the following benchmarks.
Visit the specific benchmark webpage to find related instructional resources.
Cluster Information
Number: MAFS.912.N-CN.1
Title: Perform arithmetic operations with complex numbers. (Algebra 2 - Additional Cluster)
Type: Cluster
Subject: Mathematics - Archived
Grade: 912
Cluster: Number & Quantity: The Complex Number System
Cluster Access Points
This cluster includes the following Access Points.
- MAFS.912.N-CN.1.AP.1a: Identify i as the square root of -1.
- MAFS.912.N-CN.1.AP.1b: Identify a number in the form a + bi as a complex number.
- MAFS.912.N-CN.1.AP.2a: Use properties to combine like terms of complex numbers in the form of a + bi with a and b being real numbers.
- MAFS.912.N-CN.1.AP.2b: Use properties to multiply complex numbers in the form of a + bi with a and b being real numbers.
Cluster Resources
Vetted resources educators can use to teach the concepts and skills in this topic.
Lesson Plans
- Manipulating Radicals: This lesson unit is intended to help you assess how well students are able to:
- Use the properties of exponents, including rational exponents, and manipulate algebraic statements involving radicals.
- Discriminate between equations and identities.
There is also an opportunity to consider the role of the imaginary number
, but this is optional. - Can You Hear Me Now? Using Cell Phone Signals to Divide Complex Numbers: Students always ask, “What’s the point of complex numbers?” One application of complex numbers is cell phone signals and their wavelengths. This lesson introduces division of complex numbers by hooking students in with the topic of cell phones. Students will attempt to calculate a cell phone signal wavelength involving complex numbers and discover the use of complex conjugates. Then, students will practice with complex number division using a pairing strategy. To conclude, students will use white boards and dry erase markers to review the concepts covered in class.
Problem-Solving Tasks
- Computations with Complex Numbers: This resource involves simplifying algebraic expressions that involve complex numbers and various algebraic operations.
- 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.
Tutorials
- Multiplying Complex Numbers: This video demonstrates how to multiply complex numbers using distributive property and FOIL method.
- Adding Complex Numbers: This video will demonstrate how to add complex numbers.
- Introduction to i and imaginary numbers: This video gives an introduction to 'i' and imaginary numbers. From this tutorial, students will learn the rules of imaginary numbers.