Study Guide — HSN.CN.A.3
(+) Find the conjugate of a complex number; use conjugates to find mo…
Perform arithmetic with complex numbers and represent them on the plane.
What this standard means
- (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
- Apply (+) find the conjugate of a complex number; use conjugates to find mo… with models and explanation
- Adds, subtracts, and multiplies complex numbers
_See printable PDF for diagram._
How to use the 20 practice sets
| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |
Pacing: 10–15 minutes per session.
How to practice
1. Combine like terms: real with real, imaginary with imaginary 2. Multiply using distributive property and i² = −1 3. Plot a + bi as (a, b)
_See printable PDF for diagram._
Common mistakes
- Treating i like a variable
- Sign errors in multiplication
Review and practice tests
1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for HSN.CN.A.3.
- [ ] Adds, subtracts, and multiplies complex numbers
- [ ] Uses i² = −1 correctly
- [ ] Plots complex numbers in the plane
Materials for this standard
- Practice Problems — 20 printable sets
- Review — 10 difficulty levels
- Practice Test — 10 difficulty levels
- Answer key — for parents and tutors