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

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

3. Complex Plane

4. Absolute Value (Modulus) of a Complex Number

5. Graph of z = a + bi

6. Trigonometric Form of a Complex Number

7. Example Finding Trigonometric Form

8. Example Finding Trigonometric Form

9. Product and Quotient of Complex Numbers

10. Example Multiplying Complex Numbers

11. Example Multiplying Complex Numbers

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. Example Using De Moivre’s Theorem

17. nth Root of a Complex Number

18. Finding nth Roots of a Complex Number

19. Example Finding Cube Roots

20. Example Finding Cube Roots