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Math · Algebra 2 · Unit 4

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.

Worksheets

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Unit
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Concept
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Practice
Set 1
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Set 2
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Advanced
Set 1
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Set 2
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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)
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Adapted from the Illustrative Mathematics curriculum (v.360), licensed CC BY-NC 4.0. © Illustrative Mathematics.