Imaginary Numbers

Essential Question:How do we take the square root of negative numbers?

2

2

2

i1i

• You can't take the square root of a negative number, right?

• When we were young and still in Algebra I, no numbers that, when multiplied by themselves, gave us a negative answer. 

• Squaring a negative number always gives you a positive.   (-1)² = 1. (-2)² = 4 (-3)² = 9

So here’s what the math people did: They used the letter “i” to represent the square root of (-1). “i” stands for “imaginary”

1i

So, does

1really exist?

Examples of how we use

1i

16 16 1

4 i 4i

81 81 1

9 i 9i

2

3

4

5

i

i

i

i

1i  

 

 

 

Ex: Solve x2+ 6x +10 = 0

aacbbx

242

a = 1b = 6c = 10

26 6 4 1 102 1

1st

6 36 4 1 102 1

2nd 6 36 402

6 42

6 22i

6 2 6 2

2 2i iand

3 3i and i

Ex: Solve x2+ 3x +5 = 0

aacbbx

242

a = 1b = 3c = 5

Assignment

TEXT p.206(1 – 4, 30 – 33)

“Imaginary Number”

https://youtu.be/z-ZZPzHjv8Y