1 / 25

10.7 Complex Numbers

10.7 Complex Numbers. Objective 1 . Simplify numbers of the form where b > 0 . Slide 10.7- 2. Simplify numbers of the form where b > 0. . Slide 10.7- 3. Simplify numbers of the form where b > 0. .

brinda
Télécharger la présentation

10.7 Complex Numbers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 10.7 Complex Numbers

  2. Objective 1 Simplify numbers of the form where b > 0. Slide 10.7- 2

  3. Simplify numbers of the form where b > 0. Slide 10.7- 3

  4. Simplify numbers of the form where b > 0. It is easy to mistake for with the i under the radical. For this reason, we usually write as as in the definition of Slide 10.7- 4

  5. CLASSROOM EXAMPLE 1 Simplifying Square Roots of Negative Numbers Solution: Write each number as a product of a real number and i. Slide 10.7- 5

  6. CLASSROOM EXAMPLE 2 Multiplying Square Roots of Negative Numbers Solution: Multiply. Slide 10.7- 6

  7. CLASSROOM EXAMPLE 3 Dividing Square Roots of Negative Numbers Solution: Divide. Slide 10.7- 7

  8. Objective 2 Recognize subsets of the complex numbers. Slide 10.7- 8

  9. Recognize subsets of the complex numbers. Slide 10.7- 9

  10. Recognize subsets of the complex numbers. For a complex number a + bi, if b = 0, then a + bi = a, which is a real number. Thus, the set of real numbers is a subset of the set of complex numbers. If a = 0 and b≠ 0, the complex number is said to be a pure imaginary number. For example, 3i is a pure imaginary number. A number such as 7 + 2i is a nonreal complex number. A complex number written in the form a + bi is in standard form. Slide 10.7- 10

  11. Recognize subsets of the complex numbers. The relationships among the various sets of numbers. Slide 10.7- 11

  12. Objective 3 Add and subtract complex numbers. Slide 10.7- 12

  13. CLASSROOM EXAMPLE 4 Adding Complex Numbers Solution: Add. Slide 10.7- 13

  14. CLASSROOM EXAMPLE 5 Subtracting Complex Numbers Solution: Subtract. Slide 10.7- 14

  15. Objective 4 Multiply complex numbers. Slide 10.7- 15

  16. CLASSROOM EXAMPLE 6 Multiplying Complex Numbers Solution: Multiply. Slide 10.7- 16

  17. CLASSROOM EXAMPLE 6 Multiplying Complex Numbers (cont’d) Solution: Multiply. Slide 10.7- 17

  18. CLASSROOM EXAMPLE 6 Multiplying Complex Numbers (cont’d) Solution: Multiply. Slide 10.7- 18

  19. Multiply complex numbers. The product of a complex number and its conjugate is always a real number. (a + bi)(a – bi) = a2 – b2( –1) = a2 + b2 Slide 10.7- 19

  20. Objective 5 Divide complex numbers. Slide 10.7- 20

  21. CLASSROOM EXAMPLE 7 Dividing Complex Numbers Solution: Find the quotient. Slide 10.7- 21

  22. CLASSROOM EXAMPLE 7 Dividing Complex Numbers (cont’d) Solution: Find the quotient. Slide 10.7- 22

  23. Objective 6 Find powers of i. Slide 10.7- 23

  24. Find powers of i. Because i2 = –1, we can find greater powers of i, as shown below. i3 = i · i2 = i · ( –1) = –i i4 = i2· i2 = ( –1) · ( –1) = 1 i5 = i · i4 = i · 1 = i i6 = i2· i4 = ( –1) · (1) = –1 i7 = i3· i4 = (i) · (1) = –I i8 = i4· i4 = 1 · 1 = 1 Slide 10.7- 24

  25. CLASSROOM EXAMPLE 8 Simplifying Powers of i Solution: Find each power of i. Slide 10.7- 25

More Related