1 / 71

Chapter 7

Chapter 7. 7.1 Radical Expression. Theorem 7.1. Every positive real number has two real number square roots 0 has just one square root: 0 Negative numbers do not have real number square roots. Principal Square Root.

sulwyn
Download Presentation

Chapter 7

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. Chapter 7 7.1 Radical Expression

  2. Theorem 7.1 • Every positive real number has two real number square roots • 0 has just one square root: 0 • Negative numbers do not have real number square roots

  3. Principal Square Root • The Principal Square Root of a non-negative real number is its non-negative root.

  4. This symbol is a radical sign • An expression written with a radical sign is a radical expression • The expression written under the radical sign is the radicand

  5. Radical Expression Index Radicand Radical

  6. Absolute Value • For any real number a, • The principal square root of a2 is the absolute value of a.

  7. HW 7.1Pg 295-296 1-39 Odd, 40-53

  8. Chapter 7 7.2 Multiplying and Simplifying

  9. HW 7.2Pg 299 1-47

  10. Chapter 7 7.3 Operations with Radical Expressions

  11. Chapter 7 7.4 More Operations with Radical Expressions

  12. HW 7.3-4Pg 303 1-52 Pg 308-309 1-65 Odd, 66-69

  13. Chapter 7 7.5 Rational Numbers as Exponents

  14. Theorem 7.6: For any nonnegative number a, any natural number index k, and any integer m,

  15. Definition: For any nonnegative number a and any natural number index k, means (the nonnegative kth root of a) Note: When working with rational exponents, we will assume that variables in the base are nonnegative

  16. Definition: For any natural numbers m and k, and any nonnegative number a, means

  17. Definition: For any rational number and any real number a, means

  18. HW #7.5Pg 315-316 3-75 Every third problem, 78-83

  19. Chapter 7 7.6 Solving Radical Equations

  20. Isolate the radical expression on one side of the equation.

  21. Note: When solving a radical equation it is sometimes necessary to isolate the radical and use the inverse operation more than once

  22. HW #7.6 Pg 319-320 3-39 every third problem 41-52

  23. Chapter 7 7.7 Imaginary and Complex Numbers

  24. Solve: x2 + 1 = 0 In the real number system negative numbers do not have square roots, therefore there is no real solution. x2 = -1 Mathematicians invented imaginary numbers so negative numbers would have square roots Thus the solution to the above equation would be

  25. Definition: The imaginary numbers consist of all numbers bi, where b is a real number and i is the imaginary unit, with the property that i2 = -1 Pattern Recognition Using the information from above, write a general statement about the standard form of in where n is a positive integer. Use this statement to write i231in standard form.

  26. When operating on imaginary numbers: 1. Always take the i out of the radical first 2. Treat i as a variable 3. Never write i with a power greater than 1

  27. Definition: The complex numbers consist of all sums a + bi, where a and b are real numbers and i is the imaginary unit. The real part is a and the imaginary part is bi. All real numbers are complex numbers We assume that i behaves like a real number, that is it obeys all the rules of real numbers

  28. HW #7.7Pg 323 1-33 Odd 34-63

  29. Chapter 7 7-8 Complex Numbers and Graphing

  30. Remember a complex number has a real part and an imaginary part. These are used to plot complex numbers on a complex plane. Imaginary Axis The absolute value of z denoted by |z| is the distance from the origin to the point (x, y). z b  RealAxis a

  31. Plot the number in the complex plane and then find the absolute value of the complex number.

  32. Plot the number in the complex plane and then find the absolute value of the complex number.

More Related