Complex numbers

Math

Definition

Complex numbers are numbers in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit defined as √(-1). They extend the real number system so that every polynomial equation has a solution.

Examples

  • 3 + 2i and 3 - 2i are complex conjugates
  • The solutions to x² + 1 = 0 are x = i and x = -i
  • Electrical engineers use complex numbers to analyze AC circuits
Key Fact

i = √(-1); i² = -1; i³ = -i; i⁴ = 1

Related Terms

Complex numbers in polar form Fundamental theorem of algebra Quadratic formula Discriminant

Study This Concept

Practice complex numbers with free review games in these units:

Algebra 2 Unit 3: Quadratic Functions