CCSS.Math.Content.HSN-CN.A.1
The standard
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.
Common Core State Standards for Mathematics · The Complex Number System
What this standard means
Students need to know why the number system is extended beyond real numbers. They should understand that a new unit is defined so its square is negative one. They also need to write numbers in the form real part plus imaginary part, using real values for both parts.
Mastery looks like naming the real and imaginary parts, rewriting numbers like 7, 4i, and 3 + 2i in the same form, and explaining why some equations need complex answers. Students often get stuck thinking the new unit is a variable, or thinking all complex numbers must have both parts visible.
Ways to teach it
- Use algebra tiles or a number card sort to classify 5, -2i, 3 + 4i, and 0 as complex numbers in standard form.
- Ask students to write: Why does x squared equals negative one force us to extend the real number system?
- Give four numbers and ask students to identify the real part, imaginary part, and whether either part is zero.
- Connect to electrical engineering by showing impedance written as a + bi, then have students label its real and imaginary parts.
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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.A.2
Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
- 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
Represent complex numbers and their operations on the complex plane.