Download presentation

Presentation is loading. Please wait.

Published byJoshua Fitzgerald Modified over 5 years ago

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

Similar presentations

OK

1.5 COMPLEX NUMBERS Copyright © Cengage Learning. All rights reserved.

1.5 COMPLEX NUMBERS Copyright © Cengage Learning. All rights reserved.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google