1 / 33

Complex Numbers and Operations

This lesson covers the basics of complex numbers, including operations, properties of radicals, and solving equations.

tluis
Download Presentation

Complex Numbers and Operations

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. Complex Numbers 1.1 Write Complex Numbers MM2N1a, MM2N1b

  2. Vocabulary Review • Square Root A number r is a square root of a number s if r² = s. • Radical The expression is called a radical. The symbol is a radical sign. • Radicand The number s beneath the radical sign.

  3. Properties of Radicals • Product property of radicals • Quotient property of radicals

  4. Perfect SquaresONE MINUTE!!!

  5. Perfect SquaresONE MINUTE!!!

  6. Find the greatest perfect square factor! • A. 24 • B. 42 • C. 56 • D. 18 • E. 27 • F. 68 • G. 400

  7. Simplify the expression = 4, -4 • What property is needed? The product property!

  8. Simplify the expression = ± • What property is needed? The quotient property!

  9. Simplify the expression. A. B. C. D. E. 4 4

  10. Worksheet • Odds ONLY! • Simplify # 1, 3, 5, 7 and 9. • First find the greatest perfect square factor, then simplify. • ANSWERS:

  11. How can we solve ?

  12. Worksheet • Do # 13, 15 • ANSWERS:

  13. How can we solve ?

  14. Worksheet • Do # 19, 21, 23, 25, 27, 29 • ANSWERS:

  15. Adding and Subtracting Radicals • If we have one square root of three and add two square roots of three to it, how many square roots of three do we have? • NOTE: We can only combine radicals with the same radicands. Prove this with a calculator!

  16. Worksheet • Do # 31, 33, 35 • ANSWERS:

  17. Multiplying Radicals • Use the product property of radicals and distribute.

  18. Worksheet • Do # 39, 41, 43 • ANSWERS:

  19. Dividing Radicals • Use Rationalizing the Denominator to simplify

  20. Worksheet • Do # 45, 47, 49, 51 • ANSWERS:

  21. Solving radical equations • How do we solve

  22. Worksheet • Do # 55, 57, 59, 61 • ANSWERS: 53. {96} 55. {5} 57. {-5} 59. {-5} 61. {320}

  23. Homework Worksheet even numbered problems

  24. Unit 1 – Complex Numbers • Solve

  25. Vocabulary • Imaginary Unit : i i = where i² = -1. • Complex Number Written in standard form a + bi where a and b are real numbers. The number a is the real part and the number bi is the imaginary part. • Imaginary Number If b ≠ 0, then a + bi is an imaginary number. • Pure Imaginary Number If a = 0 and b ≠ 0, then a + bi is a pure imaginary number.

  26. Write complex numbers in standard form

  27. Write the complex number in standard form.

  28. Textbook Page 4 # 13 – 15 # 16, 18, 22, 24, 26, 32

  29. Find real numbers x and y to make the equation true. 4x + 6y = 8 + 18 x = y =

  30. Find real numbers x and y to make the equation true. 4x – 4yi = 8 – 12i 5x + 3yi = 10 + 18i

  31. Find real numbers x and y to make the equation true. 8x + 8yi = 16 + 24i 2x – 7yi = -14 + 21i

  32. Textbook Page 4 #36, 38

  33. Homework Textbook Page 4 #17-45 odd

More Related