Imaginary Numbers

Algebra 2 Tutorial

Imaginary Numbers

Intro

An imaginary number is a complex number that can be written as a real number multiplied by i, which is the imaginary unit.

Sample Problem

1. Given i is the imaginary number, what is (4i-6)^2 in its simplest form?
2. What is i^24?
3. What is i^35 * i^12?

Solution

-Remember i^2 is -1.
-Remember to use FOIL.
First, Outer, Inner, and Last
1. (4i-6)^2= (4i-6)(4i-6)=16i^-2 -24i -24i +36= 16(-1)-24i-24i+36= -16-24i-24i+36= 20-48i

2. i^24 has an exponent that is the multiple of 4. Every positive i with its multiple of 4 equals to 1.
i^24=1

3. We know i^12 is 1 due to 12 being the multiple of 4, and we know i^36 is 1.
i^35= -i
i^12= 1
-i*1=-i



About The Author

Math, Biology, And History Instructor
Hello. I am Kisung Yoon, and I am a senior in high school. I am currently in the ARISTA Honor Society, and I have tutored my fellow students from my school in Algebra I, Algebra 2, Global History, US History, and Biology. Not only that, I also tutored my younger sisters on the standardized tests mai...
Send Email
10 Subjects
KnowRo Tutor
30 Tutorials
$30
Queens, NY
Learn

Suggested Tutors for Algebra 2 Help

Ad

Varsity Tutors

(855) 475-5132 - Award-Winning Academic & Test Prep Tutors

Ad

Study Wizards

(408) 883-8660 5-Star Yelp and Google in-home tutoring

Lance L

Frederick, MD

Math, Chemistry And Physics Tutor

Sophia W

Gainesville, VA

Universal Tutor

Leave a Comment

Your email address will not be published. Required fields are marked *

^