Grade 11 · Algebra & Functions
Complex Numbers
Learn to calculate with numbers that include real and imaginary parts through clear explanations, worked examples, an interactive model, and guided practice.
Lesson coverage
Learn the whole topic, not just one problem type.
This lesson and its practice bank deliberately rotate across these core facets so students build a connected understanding of the subject.
Interpret a + bi form.
Combine like components.
Use i² = −1 while multiplying.
Connect complex numbers to the plane when appropriate.
Use complex numbers in algebraic equations and models.
Build the idea
Complex Numbers is part of the extend functions and algebra to polynomial, rational, radical, exponential, logarithmic, complex, and trigonometric relationships. Start by identifying what each quantity, symbol, diagram, or graph represents before calculating.
Real & imaginary parts
Interpret a + bi form. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Addition & subtraction
Combine like components. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Multiplication
Use i² = −1 while multiplying. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Magnitude & representation
Connect complex numbers to the plane when appropriate. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Applications
Use complex numbers in algebraic equations and models. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Use a reliable strategy
Translate the information into symbols, apply one valid transformation at a time, and check the result in the original relationship.
Check and explain
A correct answer is only part of mathematical understanding. Check units, signs, scale, and whether the result makes sense. Then explain the relationship in words so you can recognize the same structure when the numbers or context change.
Key terms
Words to know
- Complex Numbers
- The central skill or relationship explored in this lesson.
- Imaginary unit
- The number i, defined by i² = −1.
- Complex number
- A number in the form a + bi.
- Real part
- The non-imaginary component of a complex number.
Interactive math lab
Change it. See it. Understand it.
Adjust the values and watch the relationship respond.
| Quantity A | 6 |
|---|---|
| Quantity B | 3 |
| Combined value | 9 |
Worked examples
See the idea in action.
Add real parts and imaginary coefficients separately.
The imaginary unit i is defined so that i² = −1.
Guided practice
20 questions drawn from a 150-question lesson bank.
Each practice session mixes the major skills in this lesson so you practice the whole topic, not just one repeated problem type.
In 1 + 1i, what is the imaginary part coefficient?
Curriculum reference
Built as a continuous K–12 progression.
The sequence follows widely used K–12 mathematics progressions and references the Common Core mathematics framework. Explanations, examples, interactive models, and practice questions are original FreeLearnHub material.