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29 March 2011

29 March 2011. Algebra 2. Shana was paid $7.79 for ¾ of an hour of work. At this rate, what is her hourly rate?. $8.54 $10.39 $5.84 $7.04. 300. 0 of 30. Congratulations!! You completed all the Interims!!!. Agenda. Bellringer Complex Numbers Review i , i x i * I

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29 March 2011

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  1. 29 March 2011 Algebra 2

  2. Shana was paid $7.79 for ¾ of an hour of work. At this rate, what is her hourly rate? • $8.54 • $10.39 • $5.84 • $7.04 300 0 of 30

  3. Congratulations!! You completed all the Interims!!!

  4. Agenda • Bellringer • Complex Numbers Review • i , • ix • i * I • Student Practice / Interim Make-up • Interim Results

  5. Complex Numbers 3/30 22 = 4 32 = 9 42 = 16 52 = 25 62 = 36 72 = 49 82 = 64 92 = 81 102 = 100 112 = 121 122 = 144 Simplifying Square Roots You should already have this list. If not, copy this list into your notes. Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  6. Complex Numbers 3/30 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 90? Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  7. Complex Numbers 3/30 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 90? 90 / 9 = 10 Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  8. Complex Numbers 3/30 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 90? 90 / 9 = 10  * = Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  9. Complex Numbers 3/30 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 90? 90 / 9 = 10  * = Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  10. Complex Numbers 3/30 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 90? 90 / 9 = 10  * = 3 * = Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  11. Complex Numbers 3/30 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 90? 90 / 9 = 10  * = 3 * = Final Answer: 3 Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  12. Simplify • 3 • 7 • 7 • 3 60 0 of 30

  13. Simplify • 4 • 5 • 10 • 2 60 0 of 30

  14. Complex Numbers 3/30 Simplify Enter on your calculator. What happens when you press enter ? Simplifying Negative Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  15. Complex Numbers 3/30 Simplify Enter on your calculator. What happens when you press enter ? Your calculator will not take the square root of a negative number. Simplifying Negative Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  16. Complex Numbers 3/30 Simplify What we need to do is deal with the negative under the radical. Simplifying Negative Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  17. Complex Numbers 3/30 Simplify What we need to do is deal with the negative under the radical. Simplifying Negative Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  18. Complex Numbers 3/30 Simplify Separate the negative sign from the number Simplifying Negative Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  19. Complex Numbers 3/30 Simplify Mathematicians invented a symbol for . = i Simplifying Negative Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  20. Complex Numbers 3/30 Simplify = i ∙ 6 Rewrite putting your number first: 6i Simplifying Negative Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  21. Simplify • 10i • 7i • 9i • 3i 60 0 of 30

  22. Simplify • 4 • 5 • 10 • 2 60 0 of 30

  23. Complex Numbers 3/30 If you raise i to a power, there are only four possible results: i1 = i2 = i3 = i4 = i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  24. Complex Numbers 3/30 If you raise i to a power, there are only four possible results: i1 = i2 = ● = -1 i3 = i4 = i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  25. Complex Numbers 3/30 If you raise i to a power, there are only four possible results: i1 = i2 = ● = -1 i3 = ● ● = - i4 = i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  26. Complex Numbers 3/30 If you raise i to a power, there are only four possible results: i1 = i2 = ● = -1 i3 = ● ● = - i4 = ● ● ● = 1 i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  27. Complex Numbers 3/30 If you raise i to a power, there are only four possible results: i1 = i2 = ● = -1 i3 = ● ● = - i4 = ● ● ● = 1 After 4, the powers start back over at 1 i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  28. Complex Numbers 3/30 i5 = ? i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  29. Complex Numbers 3/30 i5 = ? 5 – 4 = 1, so i5 = i1 i5 = i1 = i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  30. Complex Numbers 3/30 i12 = ? i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  31. Complex Numbers 3/30 i12 = ? 12 – 4 = 8 Subtract 4 i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  32. Complex Numbers 3/30 i12 = ? 12 – 4 = 8, 8 – 4 = 4 Keep subtracting 4 until you get a 1, 2, 3 or 4 i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  33. Complex Numbers 3/30 i12 = ? 12 – 4 = 8, 8 – 4 = 4, so i12 = i4 i12 = i4 = 1 i to a power Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  34. Simplify i15 • . • -1 • - • 1 0 of 30

  35. Simplify i21 • . • -1 • - • 1 0 of 30

  36. Student Practice • Complete the 20 questions from the board • You have 30 minutes to finish the assignment

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