<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />

# 5.8: Defining Complex Numbers

Difficulty Level: At Grade Created by: CK-12
Estimated10 minsto complete
%
Progress
Practice Complex Numbers

MEMORY METER
This indicates how strong in your memory this concept is
Progress
Estimated10 minsto complete
%
Estimated10 minsto complete
%
MEMORY METER
This indicates how strong in your memory this concept is

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

$i$

$i$ is an imaginary number. $i=\sqrt{-1}$.

Absolute Value

The absolute value of a number is the distance the number is from zero. The absolute value of a complex number is the distance from the complex number on the complex plane to the origin.

Complex Conjugate

Complex conjugates are pairs of complex binomials. The complex conjugate of $a+bi$ is $a-bi$. When complex conjugates are multiplied, the result is a single real number.

i

$i$ is an imaginary number. $i=\sqrt{-1}$.

Imaginary Number

An imaginary number is a number that can be written as the product of a real number and $i$.

imaginary part

The imaginary part of a complex number $a+bi$ is $bi$.

Pure Imaginary Numbers

The pure imaginary numbers are the subset of complex numbers without real parts, only $bi$.

Real Number

A real number is a number that can be plotted on a number line. Real numbers include all rational and irrational numbers.

real part

The real part of a complex number $a+bi$ is $a$.

rectangular coordinates

A point is written using rectangular coordinates if it is written in terms of $x$ and $y$ and can be graphed on the Cartesian plane.

rectangular form

The rectangular form of a point or a curve is given in terms of $x$ and $y$ and is graphed on the Cartesian plane.

standard form

The standard form of a complex number is $a+bi$ where $a$ and $b$ are real numbers.

Show Hide Details
Description
Difficulty Level:
Authors:
Tags:
Subjects: