1. Daily Check: Perform the indicated operation.
Find the area and perimeter of the box.
3. Perimeter = ____
4. Area = ____
2x-3
2x+1

2. Homework Review

3. CCGPS Analytic Geometry (8-13-14)
UNIT QUESTION: In what ways can algebraic methods be used in problem solving?
Standard: MCC9-12.N.RN.1-3, N.CN.1-3, A.APR.1
Today’s Question:
How do we take the square root of negative numbers?
Standard: MCC9-12..N.CN.1-3

4. 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

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

6. (-1) = 1
(-2) = 4
(-3) = 9

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

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

9. Ladies and Gentlemen of Math II
I present to you
a NEW number...
A number so complex...

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

12. You can't take the square root of a negative number, right?
When we were young and still in Math 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

13. 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?

14. Examples of how we use

15. Examples of how we use

17. 1.3 Powers of i and Complex Operations

18. *For larger exponents, divide the exponent by 4, then use the remainder as your exponent instead.
Example:

20. Complex Numbers A complex number has a real part & an imaginary part.
Standard form is:
Real part
Imaginary part
Example: 5+4i

21. Adding and Subtracting Add or subtract the real parts, and then, add or subtract the imaginary parts.
Ex:
Ex:

22. Your Turn!

23. Your Turn!

24. Multiplying Treat the i’s like variables, then change any that are not to the first power
Ex:
Ex:

25. Your Turn!

26. Your Turn!

27. Conjugates: Two complex numbers of the form a + bi and a – bi are complex conjugates. The product is always a real number
Ex:

28. Conjugates: Two complex numbers of the form a + bi and a – bi are complex conjugates. The product is always a real number
Ex:

29. Dividing Complex Numbers

30. Conjugates: Two complex numbers of the form a + bi and a – bi are complex conjugates. The product is always a real number

31. Dividing Complex Numbers
Multiply the numerator and denominator by the conjugate of the denominator.
Simplify completely.

32. Writing in Standard Form

33. Your Turn!

34. Your Turn!

35. Assignment
Complex Numbers Practice WS