CCSS.Math.Content.HSN-CN.B

MathGrades 9–12The Complex Number System

The standard

Represent complex numbers and their operations on the complex plane.

Common Core State Standards for Mathematics

What this standard means

Students need to treat a complex number as a point or vector, with the real part on the horizontal axis and the imaginary part on the vertical axis. They should graph numbers like 3 + 2i, find sums and differences by moving on the plane, and connect multiplication to scaling and rotation.

Mastery looks like switching between a + bi, ordered pairs, and points on the plane without confusion. Students often mix up axes, forget that i is not a variable, or can add coordinates but cannot explain what the movement means.

Ways to teach it

  • Use graph paper and colored arrows to model adding 2 + 3i and -4 + i as vector moves on the complex plane.
  • Ask students to write how adding complex numbers is like adding ordered pairs, and where the comparison breaks down.
  • Give four complex numbers and have students plot them, then label their real part, imaginary part, and quadrant.
  • Connect multiplication by i to a 90-degree rotation using a simple point like 4 + 0i on a coordinate grid.

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Related standards

  • CCSS.Math.Content.HSN-CN.C

    Use complex numbers in polynomial identities and equations.

  • CCSS.Math.Content.HSN-CN.B.4

    (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and pol...

  • 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.

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

Page updated July 10, 2026.

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