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



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