CCSS.Math.Content.HSN-CN.A.2
The standard
Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
Common Core State Standards for Mathematics · The Complex Number System
What this standard means
Students need to treat complex numbers like binomials, while remembering that i squared equals negative 1. They should add and subtract by combining real parts and imaginary parts, then multiply using distribution or a box method.
Mastery looks like clean simplification to a plus bi form, with correct signs. Students often forget to replace i squared, combine unlike terms, or lose negatives when subtracting parentheses. Multiplication errors usually come from rushing FOIL or stopping before simplifying.
Ways to teach it
- Use algebra tiles labeled 1, i, and negative 1 to model adding, subtracting, and multiplying simple complex numbers.
- Ask students to explain why (3 plus 2i)(4 minus i) is not finished until the i squared term is simplified.
- Give a five-problem exit ticket with two sums, one difference, and two products written in a plus bi form.
- Connect complex multiplication to electrical engineering by showing how AC circuit calculations use real and imaginary parts together.
Plan a lesson for CCSS.Math.Content.HSN-CN.A.2
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.HSN-CN.B
Represent complex numbers and their operations on the complex plane.
- CCSS.Math.Content.HSN-CN.A.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.
- CCSS.Math.Content.HSN-CN.B.5
(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representatio...
- CCSS.Math.Content.HSN-CN.A
Perform arithmetic operations with complex numbers.