## 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

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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... |