1. Copyright © 2011 Pearson, Inc. P.6 Complex Numbers

2. Copyright © 2011 Pearson, Inc. Slide P.6 - 2 What youll learn about Complex Numbers Operations with Complex Numbers Complex Conjugates and Division Complex Solutions of Quadratic Equations … and why The zeros of polynomials are complex numbers.

3. Copyright © 2011 Pearson, Inc. Slide P.6 - 3 Complex Number A complex number is any number that can be written in the form a + bi, where a and b are real numbers. The real number a is the real part, the real number b is the imaginary part, and a + bi is the standard form.

4. Copyright © 2011 Pearson, Inc. Slide P.6 - 4 Addition and Subtraction of Complex Numbers If a + bi and c + di are two complex numbers, then Sum: (a + bi ) + (c + di ) = (a + c) + (b + d)i, Difference: (a + bi ) – (c + di ) = (a – c) + (b –d)i.

5. Copyright © 2011 Pearson, Inc. Slide P.6 - 5 Example Multiplying Complex Numbers

6. Copyright © 2011 Pearson, Inc. Slide P.6 - 6 Solution

7. Copyright © 2011 Pearson, Inc. Slide P.6 - 7 Complex Conjugate

8. Copyright © 2011 Pearson, Inc. Slide P.6 - 8 Complex Numbers The multiplicative identity for the complex numbers is 1 = 1 + 0i. The multiplicative inverse, or reciprocal, of z = a + bi is

9. Copyright © 2011 Pearson, Inc. Slide P.6 - 9 Example Dividing Complex Numbers

10. Copyright © 2011 Pearson, Inc. Slide P.6 - 10 Solution the complex number in standard form.

11. Copyright © 2011 Pearson, Inc. Slide P.6 - 11 Discriminant of a Quadratic Equation

12. Copyright © 2011 Pearson, Inc. Slide P.6 - 12 Example Solving a Quadratic Equation

13. Copyright © 2011 Pearson, Inc. Slide P.6 - 13 Example Solving a Quadratic Equation

14. Copyright © 2011 Pearson, Inc. Slide P.6 - 14 Quick Review

15. Copyright © 2011 Pearson, Inc. Slide P.6 - 15 Quick Review Solutions