CCSS.Math.Content.HSN-CN.A

MathGrades 9–12The Complex Number System

The standard

Perform arithmetic operations with complex numbers.

Common Core State Standards for Mathematics

What this standard means

Students need to add, subtract, and multiply numbers that include an imaginary part, like 3 + 2i. They should combine like terms, use the distributive property, and replace i² with -1 when it appears. They also need to understand that real numbers fit inside this larger number system.

Mastery looks like clean, accurate simplification with clear steps and correct use of i² = -1. Students often get stuck treating i like a variable only, forgetting to simplify i², or losing negative signs during multiplication. They may also mix up real and imaginary parts when combining terms.

Ways to teach it

  • Use algebra tiles or colored index cards to model real parts and imaginary parts, then have students combine and multiply simple complex numbers.
  • Ask students to explain why i² = -1 changes the result of (2 + 3i)(4 - i).
  • Give a 5-question exit ticket with two sums, one difference, and two products of complex numbers.
  • Connect complex numbers to electrical circuits by showing how engineers use real and imaginary parts to describe impedance.

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Related standards

Standard text verified against corestandards.org on July 10, 2026.

Page updated July 10, 2026.

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