De Moivre’s Theorem and n th Roots

1. Precalculus Lesson 6.6 De Moivre’s Theorem and nth Roots

2. Quick Review

3. Quick Review

4. 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 zn = c, n is an integer and c is a complex number.

5. Complex Plane Imaginary axis Example Imaginary axis Real axis Real axis

6. Absolute Value (Modulus) of a Complex Number

7. Graph of z = a + bi

8. Trigonometric Form of a Complex Number

9. Example Finding Trigonometric Form

10. Product and Quotient of Complex Numbers

11. Example Multiplying ComplexNumbers

12. A Geometric Interpretation of z2

13. De Moivre’s Theorem

14. Example Using De Moivre’s Theorem

15. Example Using De Moivre’s Theorem

16. nth Root of a Complex Number

17. Finding nth Roots of a Complex Number

18. Example Finding Cube Roots

19. Example Finding Cube Roots They are evenly spaced (with distance of 2π/3 radians) around the unit circle.

20. Homework: Text pg558 Exercises #5,16,17,22,26,37,38,41