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

2. Homework Review

3. CCGPS Analytic Geometry Day 32 (9-20-13) 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

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

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. The Complex Plane Imaginary Axis Real Axis

22. Graphing in the complex plane

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

24. Your Turn!

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

27. Your Turn!

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

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

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

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

34. Writing in Standard Form

35. Your Turn!

37. Assignment Complex Numbers Practice WS