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

Equations and Inequalities



SOL Review Materials
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. Notes: Complex Numbers (flipchart)
Real World Lessons
  1. VDOE ESS: Powers of i Table (pdf)
  2. VDOE ESS: Complex Numbers Worksheet (pdf)
  3. VDOE ESS: Complex Numbers Extension (pdf)
  4. Worksheet: Complex Numbers (doc)
  1. SOL Mini-Quiz: AII.3 - Operations with Complex Numbers
  1. JMU Pivotal Question: Complex Operations (doc)
  1. Video Tutor - Complex Numbers
  2. Video Notes: Complex Numbers
Explore Learning
  1. None
  1. Notes:- Complex Numbers Introduction from
  2. Notes/Activity: Complex Numbers from
Common Core Standards