Download presentation

Presentation is loading. Please wait.

Published byCayla Curl Modified over 3 years ago

1
**6.10 Simplifying Expressions Containing Complex Numbers**

Algebra 2 Mrs. Spitz Spring 2007

2
Objective Simplify rational expressions containing complex numbers in the denominator.

3
**Assignment Pgs. 299-300 #5-61 odd only**

Chapter 6 Review. Pgs # Bring your questions to class so you are prepared next time we test. Chapter 6 notes are due in your binder on test date.

4
Note: As you know, two radical expressions of the form a√b + c √d and a √b – c √d are conjugates of each other. Since imaginary numbers involve radicals, numbers of the form a + bi and a – bi are also called conjugates. Recall that the product of two radical conjugates is a rational number. Let’s investigate the product of two complex conjugates.

5
**Ex. 1: Find the product of the conjugates 5 + 2i and 5 – 2i.**

(5 + 2i)(5 – 2i) = 25 – 10i + 10i -4i2 = 25 – 4(-1) = = 29 Reminder: i2 = -1

6
**Ex. 2: Find the product of the conjugates a + bi and a – bi.**

(a + bi)(a – bi) = a2 – abi + abi - bi2 = a2 –bi2 = a2 – b2(-1) = a2 +b2 Reminder: i2 = -1 Since a and b are real, a2b2 will also be real.

7
Note: To simplify expressions, we must eliminate all radicals in the denominator. Since i is a radical, all imaginary numbers must also be eliminated from denominators. Ex. 3: Simplify If you wanted to multiply by –i/-i, you could have.

8
**Rationalizing the denominator**

We use conjugates of radicals to rationalize the denominators of expressions with radicals in the denominator. We can also use conjugates of complex numbers to rationalize the denominators of expressions with complex numbers in the denominator.

9
Ex. 4: Simplify

10
**Ex. 5: Find the multiplicative inverse of 5 – 7i.**

The multiplicative inverse of 5 – 7i is

11
**Ex. 5: Check your work! The inverse of 5 – 7i is**

The multiplicative inverse of 5 – 7i is The inverse of 5 – 7i is

12
Reminder: Review over chapter 6 followed by the exam. Bring your questions to class next time we meet. We will not be doing the review in class. It is an assignment due after you turn in your test. Don’t forget your chapter 6 notes in your binder for me to check.

Similar presentations

OK

Simplifying Radical Expressions Basic multiplication Basic division o Rationalize the denominator.

Simplifying Radical Expressions Basic multiplication Basic division o Rationalize the denominator.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on diabetes in hindi Ppt on marie curie cancer Ppt on windows vista operating system Ppt on object oriented programming in java Download ppt on social problems in india Ppt on mass media services Ppt on preparation and properties of alcohols and phenols Ppt on juvenile rheumatoid arthritis Ppt on air pressure and wind system Ppt on balanced diet