1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 1 Homework, Page 548 (a) Complete the table for the equation and (b) plot the points. 1. θ0π/4π/23π/4π5π/43π/27π/4 r30–3030 0

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 2 Homework, Page 548 Draw the graph of the rose curve. State the smallest θ-interval (0 ≤ θ ≤ k) that will produce a complete graph. 5.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 3 Homework, Page 548 Match the equation with its graph without using your calculator. 9.

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 4 Homework, Page 548 Use the polar symmetry tests to determine if the graph is symmetric about the x-axis, the y-axis, or the origin.. 13.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 5 Homework, Page 548 Use the polar symmetry tests to determine if the graph is symmetric about the x-axis, the y-axis, or the origin.. 17.

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 6 Homework, Page 548 Identify the points on 0 ≤ θ ≤ 2π where maximum r-values occur. 21.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 7 Homework, Page 548 Analyze the graph of the polar curve. 25. Domain: Range: Continuity: Symmetry: Boundedness: Maximum r-value: Asymptotes:

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 8 Homework, Page 548 Analyze the graph of the polar curve. 29. Domain: Range: Continuity: Symmetry: Boundedness: Maximum r-value: Asymptotes:

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 9 Homework, Page 548 Analyze the graph of the polar curve. 33. Domain: Range: Continuity: Symmetry: Boundedness: Maximum r-value: Asymptotes:

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 10 Homework, Page 548 Analyze the graph of the polar curve. 37. Domain: Range: Continuity: Symmetry: Boundedness: Maximum r-value: Asymptotes:

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 11 Homework, Page 548 Analyze the graph of the polar curve. 41. Domain: Range: Continuity: Symmetry: Boundedness: Maximum r-value: Asymptotes:

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 12 Homework, Page 548 Find the length of each petal of the polar curve. 45.

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 13 Homework, Page 548 Select the two equations whose graphs are the same curve. Then, describe how the paths are different as θ increases from 0 to 2π. 49.

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 14 Homework, Page 548 (a) Describe the graph of the polar equation, (b) state any symmetry the graph possesses, and (c) state the maximum r- value, if it exists. 53. (a) The graph of the polar equation has two large petals and two small petals. (b) The graph is symmetric about the origin. (c) The maximum r-value is 3.

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 15 Homework, Page 548 57. Domain: Range: Continuity: Symmetry: Boundedness: Maximum r-value: Asymptotes:

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 16 Homework, Page 548 61. A polar curve is always bounded. Justify your answer. False The spiral curve, the graph of the polar equation r = θ is unbounded.

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 17 Homework, Page 548 65. Which of the following is the maximum r-value for r = 2 – 3 cos θ? a.6 b.5 c.3 d.2 e.1

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 18 Homework, Page 548 69.

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 6.6 De Moivre’s Theorem and nth Roots

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 20 Quick Review

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 21 Quick Review Solutions

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 22 What you’ll learn about The Complex Plane Trigonometric Form of Complex Numbers Multiplication and Division of Complex Numbers Powers of Complex Numbers Roots of Complex Numbers … and why The material extends your equation-solving technique to include equations of the form z n = c, n is an integer and c is a complex number.

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 23 Complex Plane

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 24 Addition of Complex Numbers

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 25 Absolute Value (Modulus) of a Complex Number

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 26 Graph of z = a + bi

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 27 Trigonometric Form of a Complex Number

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 28 Example Finding Trigonometric Form

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 29 Product and Quotient of Complex Numbers

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 30 Example Multiplying Complex Numbers

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 31 Example Dividing Complex Numbers

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 32 A Geometric Interpretation of z 2

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 33 De Moivre’s Theorem

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 34 Example Using De Moivre’s Theorem

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 35 nth Root of a Complex Number

36. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 36 Finding nth Roots of a Complex Number

37. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 37 Example Finding Cube Roots

38. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 38 Homework Homework Assignment #8 Review Section: 6.6 Page 559, Exercises: 1 – 69 (EOO), 81, 83 Quiz next time