Algebra 2 Online!
Henrico County Public Schools, Virginia
Expressions and Operations

Equations and Inequalities

Functions

Statistics

SOL Review Materials
AII.3
The student will perform operations on complex numbers, express the results in simplest form using patterns of the powers of i, and identify field properties that are valid for the complex numbers.
Essential Knowledge and Skills 
  • Recognize that the square root of –1 is represented as i.
  • Determine which field properties apply to the complex number system.
  • Simplify radical expressions containing negative rational numbers and express in a+bi form.
  • Simplify powers of i.
  • Add, subtract, and multiply complex numbers.
  • Place the following sets of numbers in a hierarchy of subsets: complex, pure imaginary, real, rational, irrational, integers, whole, and natural.
  • Write a real number in a+bi form.
  • Write a pure imaginary number in a+bi form.
Essential Understandings
  • Complex numbers are organized into a hierarchy of subsets.
  • A complex number multiplied by its conjugate is a real number.
  • Equations having no real number solutions may have solutions in the set of complex numbers.
  • Field properties apply to complex numbers as well as real numbers.
  • All complex numbers can be written in the form a+bi where a and b are real numbers and i is the square root of -1.
Vertical Articulation
  1. SOL A.2 - a) apply laws of exponents to perform ops on expressions;
    b) add/subtract/multiply/divide polynomials; c) factor first and second degree binomials/trinomials (1 or 2 variables)
Instructional Materials
  1. VDOE ESS Lesson: Complex Numbers - Expressions and Operations (PDF) - Performing complex number arithmetic (Word)
  2. Warm-up: Classifying Numbers (flipchart)
  3. Interactive Notes: Properties (flipchart)
  4. Properties Guided Notes (doc)
Real World Lessons
Practice
  1. VDOE ESS: Complex Numbers Worksheet (pdf)
  2. Worksheet: Properties (doc)
Self-Assessments
  1. SOL Mini-Quiz: AII.3 Properties of Complex Numbers
Skills
  1. JMU Pivotal Question: Powers of i (doc)
Videos
  1. Video Tutor - Complex Numbers
Explore Learning
  1. None
Websites
  1. Notes:- Complex Numbers Introduction from Purplemath.com
  2. Notes/Activity: Complex Numbers from Regentsprep.com
Common Core Standards
N-CN.1
N-CN.2
N-CN.3