Unit 4: Complex Numbers and Rational Exponents

Students extend exponent rules to rational exponents, solve equations involving square and cube roots, develop the concept of complex numbers, and solve quadratic equations with real or complex solutions.

Choose a worksheet

PDFs open in a new tab. Print or save them from your browser. Use the paired answer guide to check your work. No login needed.

Unit

Review the unit’s main ideas.

📝 Open worksheet PDF ✅ Open answer guide PDF

Concept

Start with the core idea.

📝 Open worksheet PDF ✅ Open answer guide PDF

Practice

Build fluency with more questions.

Set 1

📝 Open worksheet PDF ✅ Open answer guide PDF

Set 2

📝 Open worksheet PDF ✅ Open answer guide PDF

Advanced

Try more challenging problems.

Set 1

📝 Open worksheet PDF ✅ Open answer guide PDF

Set 2

📝 Open worksheet PDF ✅ Open answer guide PDF

What this unit covers

A Exponent Properties · 5 lessons

Goals

• Use both radicals and exponents to represent numbers.

Lessons

1. Properties of Exponents (Optional)
2. Square Roots and Cube Roots (Optional)
3. Exponents That Are Unit Fractions
4. Positive Rational Exponents
5. Negative Rational Exponents

B Solving Equations with Square and Cube Roots · 4 lessons

Goals

• Calculate solutions to radical equations.
• Explain why a radical equation has 0 solutions or 1 solution.

Lessons

1. Squares and Square Roots
2. Inequivalent Equations?
3. Cubes and Cube Roots
4. Solving Radical Equations (Optional)

C A New Kind of Number · 6 lessons

Goals

• Add, subtract, and multiply complex numbers, and represent the solutions in the form a + bi.

Lessons

1. A New Kind of Number
2. Introducing the Number i
3. Arithmetic with Complex Numbers
4. Multiplying Complex Numbers
5. More Arithmetic with Complex Numbers (Optional)
6. Working Backward

D Solving Quadratics with Complex Numbers · 4 lessons

Goals

• Create quadratic equations that have either real or non-real solutions.
• Solve quadratic equations, and explain the solution method.

Lessons

1. Solving Quadratics (Optional)
2. Completing the Square and Complex Solutions
3. The Quadratic Formula and Complex Solutions
4. Real and Non-Real Solutions (Optional)

E Let's Put It to Work · 1 lesson

Lessons

1. Drawing Proportional Circles (Optional)