# 5.8: Defining Complex Numbers

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**Practice**Complex Numbers

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is an imaginary number. .

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 is . When complex conjugates are multiplied, the result is a single real number.i

is an imaginary number. .Imaginary Number

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

The imaginary part of a complex number is .Pure Imaginary Numbers

The pure imaginary numbers are the subset of complex numbers without real parts, only .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 is .rectangular coordinates

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

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

The standard form of a complex number is where and are real numbers.### Image Attributions

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This lesson covers the powers of i, adding, and subtracting complex numbers.

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Date Created:

Mar 12, 2013
Last Modified:

Sep 07, 2016
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