1. Sec. 6.6b

2. One reason for writing complex numbers in trigonometric form is the convenience for multiplying and dividing: T The product i i i involves the product of the moduli and the sum of the arguments he quotient involves the quotient of the moduli and the difference of the arguments

3. Let and 1.. Then 2.,

4. Express the product of the given complex numbers in standard form: Product:

5. Express the quotient of the given complex numbers in standard form: Quotient:

6. Express the product of the given complex numbers in trigonometric form:

7. Express the quotient of the given complex numbers in trigonometric form:

8. Find the product and quotient of the given complex numbers in two ways, (a) using standard forms, and (b) using trig. forms. The product: The quotient:

9. Find the product and quotient of the given complex numbers in two ways, (a) using standard forms, and (b) using trig. forms. Next, find the trigonometric forms: The product: The quotient:

10. First, let’s look at a problem: Real Axis Imaginary Axis z z 2 Graphically: rr 2

11. Now, let’s find the cube of z: And the pattern continues for higher powers:

12. De Moivre’s Theorem This pattern is generalized to give: Let and let n be a positive integer. Then

13. Find using De Moivre’s Theorem. Begin with a graph: Modulus r = 2 Argument

14. Find using De Moivre’s Theorem. Verify with your calculator!!! 

15. Find using De Moivre’s Theorem. Convert to trig. form:

16. The complex number is a third root of –8 The complex number is an eighth root of 1

17. Use De Moivre’s Theorem to find the indicated power of the given complex number. Write your answer in standard form.

18. Use De Moivre’s Theorem to find the indicated power of the given complex number. Write your answer in standard form.

19. Use De Moivre’s Theorem to find the indicated power of the given complex number. Write your answer in standard form.

20. Use De Moivre’s Theorem to find the indicated power of the given complex number. Write your answer in standard form.