Download presentation

Presentation is loading. Please wait.

Published byEric Morris Modified over 5 years ago

1
Chapter 2 Polynomial and Rational Functions

2
Warm Up 2.4 From 1980 to 2002, the number of quarterly periodicals P published in the U.S. can be modeled by Where t is the number of years since 1980. a. Describe the end behavior of the graph. b. Graph the model on the domain 0 ≤ t ≤ 22. c. Use the model to predict the number of quarterly periodicals in the year 2010. 2

3
2.4 Complex Numbers Objectives: Use the imaginary unit i to write complex numbers. Add, subtract, and multiply complex numbers. Use complex conjugates to write the quotient of two complex numbers in standard form. Plot complex numbers in the complex plane. 3

4
The Imaginary Unit, i If we find the square root of a number, are there any restrictions? Yes – the term inside the radical must be ≥ 0. What happens if the term inside the radical is negative? For example, what if x 2 + 1 = 0 ? This equation has no real solution. The Imaginary Unit i was created for this purpose. That is, and 4

5
Complex Numbers A complex number consists of a real part and an imaginary part. Standard form of a complex number is a ± bi, where a is the real part and bi is the imaginary part. 5

6
Adding and Subtracting Complex Numbers Add or subtract the real parts and add or subtract the imaginary parts. 6

7
Examples Perform the following operations. Simplify if possible. 7

8
Multiplying Complex Numbers FOIL or distribute and simplify. Note: Be sure numbers are written in complex form before you begin. 8

9
Examples Perform the following operations. Simplify if possible. 9

10
Imaginary Units of Higher Power How can we easily find i raised to any integer power? What is the next one? What is the pattern? 10

11
Complex Conjugates The product of two complex numbers is usually another complex number. However, the product of two complex numbers can be a real number if the two numbers are conjugates. Numbers of the form a + bi and a – bi are complex conjugates. 11

12
Example Multiply 3 – 5i by its complex conjugate. 12

13
Complex Number Quotients When we divide a complex number by another complex number, we can write it as a quotient. We want to make sure that the denominator is real, not imaginary or complex. To do so, we must multiply both the numerator and the denominator of the quotient by the complex conjugate of the denominator. 13

14
Example Write the quotient in standard form. 14

15
Homework 2.4 Worksheet 2.4 #5, 9, 11, 17 – 35 odd, 37, 45 – 61 odd 15

Similar presentations

© 2020 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