1. Copyright © 2011 Pearson, Inc. 6.6 Day 1 De Moivres Theorem and nth Roots Goal: Represent complex numbers in the complex plane and write them in trigonometric form.

2. Copyright © 2011 Pearson, Inc. Slide 6.1 - 2 What youll learn about The Complex Plane (Day 1) Trigonometric Form of Complex Numbers (Day 1) Multiplication and Division of Complex Numbers (Day 2) Powers of Complex Numbers (Day 3) Roots of Complex Numbers (Day 3) … 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. Plotting Complex Numbers

4. Copyright © 2011 Pearson, Inc. Plot the following complex numbers and state the absolute value of the number.

5. Copyright © 2011 Pearson, Inc. Which complex number corresponds to each point plotted below?

6. Copyright © 2011 Pearson, Inc. RectangularPolarComplexTrig Form Coordinates of a point Horizontal axis Vertical axis intersection of axes

7. Copyright © 2011 Pearson, Inc. Convert 3 + 3i to the following forms… Rectangular: Polar: Trigonometric:

8. Copyright © 2011 Pearson, Inc. Convert (5, 12) to the following forms… Complex: Polar: Trigonometric:

9. Copyright © 2011 Pearson, Inc. Trigonometric: Rectangular: Complex:

10. Copyright © 2011 Pearson, Inc. Polar: Complex: Rectangular: