1. Copyright © 2011 Pearson, Inc. 6.6 De Moivre’s Theorem and nth Roots

2. Copyright © 2011 Pearson, Inc. Slide 6.1 - 2 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.

3. Copyright © 2011 Pearson, Inc. Slide 6.1 - 3 Complex Plane

4. Copyright © 2011 Pearson, Inc. Slide 6.1 - 4 Absolute Value (Modulus) of a Complex Number

5. Copyright © 2011 Pearson, Inc. Slide 6.1 - 5 Graph of z = a + bi

6. Copyright © 2011 Pearson, Inc. Slide 6.1 - 6 Trigonometric Form of a Complex Number

7. Copyright © 2011 Pearson, Inc. Slide 6.1 - 7 Example Finding Trigonometric Form

8. Copyright © 2011 Pearson, Inc. Slide 6.1 - 8 Example Finding Trigonometric Form

9. Copyright © 2011 Pearson, Inc. Slide 6.1 - 9 Product and Quotient of Complex Numbers

10. Copyright © 2011 Pearson, Inc. Slide 6.1 - 10 Example Multiplying Complex Numbers

11. Copyright © 2011 Pearson, Inc. Slide 6.1 - 11 Example Multiplying Complex Numbers

12. Copyright © 2011 Pearson, Inc. Slide 6.1 - 12 A Geometric Interpretation of z 2

13. Copyright © 2011 Pearson, Inc. Slide 6.1 - 13 De Moivre’s Theorem

14. Copyright © 2011 Pearson, Inc. Slide 6.1 - 14 Example Using De Moivre’s Theorem

15. Copyright © 2011 Pearson, Inc. Slide 6.1 - 15 Example Using De Moivre’s Theorem

16. Copyright © 2011 Pearson, Inc. Slide 6.1 - 16 Example Using De Moivre’s Theorem

17. Copyright © 2011 Pearson, Inc. Slide 6.1 - 17 nth Root of a Complex Number

18. Copyright © 2011 Pearson, Inc. Slide 6.1 - 18 Finding nth Roots of a Complex Number

19. Copyright © 2011 Pearson, Inc. Slide 6.1 - 19 Example Finding Cube Roots

20. Copyright © 2011 Pearson, Inc. Slide 6.1 - 20 Example Finding Cube Roots