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# 4.5: Complex Numbers

Difficulty Level: At Grade Created by: CK-12
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### Vocabulary Language: English

$i$

$i$

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

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 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.
complex number

complex number

A complex number is the sum of a real number and an imaginary number, written in the form $a + bi$.
complex plane

complex plane

The complex plane is the graphical representation of the set of all complex numbers.
i

i

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

Real Number

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

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

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.
superset

superset

A superset is a set that includes other sets within it. The complex number set includes all classic complex numbers $a+bi$, and also, because $bi$ may equal 0, it includes all of the real numbers as well. This makes it a '''superset''' of the set of real numbers.

Nov 01, 2012

Jun 08, 2015