Algebra
Textbooks
Boundless Algebra
Complex Numbers and Polar Coordinates
Algebra Textbooks Boundless Algebra Complex Numbers and Polar Coordinates
Algebra Textbooks Boundless Algebra
Algebra Textbooks
Algebra

Section 2

Complex Numbers

Book Version 13
By Boundless
Boundless Algebra
Algebra
by Boundless
View the full table of contents
7 concepts
Thumbnail
Introduction to Complex Numbers

A complex number has the form $a+bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit.

Addition and Subtraction of Complex Numbers

Complex numbers can be added and subtracted by adding the real parts and imaginary parts separately. 

Multiplication of Complex Numbers

Complex numbers can be multiplied using the FOIL algorithm.

Complex Numbers and the Binomial Theorem

Powers of complex numbers can be computed with the the help of the binomial theorem.

Thumbnail
Complex Conjugates

The complex conjugate of the number $a+bi$ is $a-bi$. Two complex conjugates of each other multiply to be a real number with geometric significance. 

Division of Complex Numbers

Division of complex numbers is accomplished by multiplying by the multiplicative inverse. The multiplicative inverse of $z$ is $\frac{\overline{z}}{\abs{z}^2}.$

Thumbnail
Complex Numbers in Polar Coordinates

Complex numbers can be represented in polar coordinates using the formula $a+bi=re^{i\theta}$. This leads to a way to visualize multiplying and dividing complex numbers geometrically.

Subjects
  • Accounting
  • Algebra
  • Art History
  • Biology
  • Business
  • Calculus
  • Chemistry
  • Communications
  • Economics
  • Finance
  • Management
  • Marketing
  • Microbiology
  • Physics
  • Physiology
  • Political Science
  • Psychology
  • Sociology
  • Statistics
  • U.S. History
  • World History
  • Writing

Except where noted, content and user contributions on this site are licensed under CC BY-SA 4.0 with attribution required.