1. 1-3 Imaginary Numbers

2. in a math class far, far away..
A long long time ago,
in a math class far, far away..
There was no way
to take the square root
of a negative number

3. Every time we squared a negative number
We got a positive.

4. (-1) = 1
(-2) = 4
(-3) = 9

5. that when multiplied by itself
Was there a number,
that when multiplied by itself
Gave you a negative???

6. Can we in fact, take the square root
of a negative number?
WE CAN!!!!

7. Ladies and Gentlemen of Geometry
I present to you
a NEW number...
A number so complex...

8. It stretches the imagination..
I present to you:

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

12. Examples of how we use

13. Examples of how we use

14. Radicals and Fractions
You can rearrange the radical sign. =
reduce fraction first = 5
OR separate first = = 5 6

15. Simplify

16. Powers of i

17. Simplify.

18. Complex Numbers Example: 5+4i Standard form is: Real part
Imaginary part