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Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9.7 - 1
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9.7 - 2
Roots, Radicals, and Root Functions
Chapter 9
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9.7 - 3
9.7
Complex Numbers
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 4
9.7 Complex Numbers
Objectives
1. Simplifying numbers of the form , where b >0.
2. Recognize subsets of the complex numbers.
3. Add and subtract complex numbers.
4. Multiply complex numbers.
5. Divide complex numbers.
6. Find powers of i.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 5
9.7 Complex Numbers
Simplify Numbers of the Form , Where b >0
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 6
9.7 Complex Numbers
Simplify Numbers of the Form , where b >0
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 7
9.7 Complex Numbers
Simplify Numbers of the Form , where b >0
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 8
9.7 Complex Numbers
Multiplying Square Roots of Negative Numbers
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 9
9.7 Complex Numbers
Multiplying Square Roots of Negative Numbers
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 10
9.7 Complex Numbers
Dividing Square Roots of Negative Numbers
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 11
9.7 Complex Numbers
Recognize Subsets of the Complex Numbers
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 12
9.7 Complex Numbers
Recognize Subsets of the Complex Numbers
Imaginary part of the number
Real part of the number
Examples:
Pure imaginary
number
All written in standard form
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 13
9.7 Complex Numbers
Adding and Subtracting Complex Numbers
Adding
Subtracting
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 14
9.7 Complex Numbers
Multiplying Complex Numbers
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 15
9.7 Complex Numbers
Multiplying Complex Numbers
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 16
9.7 Complex Numbers
Multiplying Complex Numbers
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 17
9.7 Complex Numbers
Dividing Complex Numbers
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 18
9.7 Complex Numbers
Dividing Complex Numbers
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 19
9.7 Complex Numbers
Simplifying Powers of i
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.7 - 20
9.7 Complex Numbers
Simplifying Powers of i
Examples:
