Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
9.1 complex numbers 2016 ink.notebook page 53 ch 7 Exponents Fill in your pre and post test results February 21, 2017 Post test Pretest number correct: total number of problems: number correct: total number of problems: Percentage correct: Percentage correct: Change in percentage: Page 73 difference original = Page 74 Page 72 Unit 9 Radicals 9.1 Complex Numbers 1 9.1 complex numbers 2016 ink.notebook February 21, 2017 Page 76 Page 75 Lesson Objectives Standards Lesson Notes 9.1 Complex Numbers Press the tabs to view details. Lesson Objectives Standards Lesson Notes Lesson Objectives A.SSE.2 Standards Lesson Notes I will rewrite a complex expression in simplest form A.SSE.2. Use the structure of an expression to identify ways to rewrite it. N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Press the tabs to view details. Press the tabs to view details. 2 9.1 complex numbers 2016 ink.notebook February 21, 2017 Not all radicals have real number solutions. Mathematicians created an expanded number system using the imaginary unit i. The imaginary unit i can be used to write the square root of any negative number and is defined It follows then A complex number written in standard form is the number a + bi where a is the real number part and bi is the imaginary part. Identify real number parts and imaginary number parts. 1. 7 + 3i 2. 8 – i 3. 5i 4. 2 3 9.1 complex numbers 2016 ink.notebook Complex Numbers (imaginary numbers) i i = 2 -1 = -1 February 21, 2017 A negative on the inside Pulls an i to the outside -4 = 2i - -16 = -4i -5 = 2 i 5 (3i ) = 32 i 9 -1 = -9 2 Examples. Solve each: 5. 6. 7. 8. 9. 10. 4 9.1 complex numbers 2016 ink.notebook February 21, 2017 Examples. Solve each: 11. 12. 13. 14. 15. 16. Parts of a Radical radical symbol index 36 radicand Converting between Radical Form and Rational Exponent Form i x e e =xi exponent over index 1 radical If the index is not written, it is automatically a 2. 2 1 81 = 2 81 = 81 3 4 3 4 81 = 81 5 9.1 complex numbers 2016 ink.notebook February 21, 2017 21. 22. Write each expression in radical form. 17. 18. 23. 19. 24. 20. 25. 27. 26. 28. 6 9.1 complex numbers 2016 ink.notebook 29. 30. 31. 32. On Your Whiteboards February 21, 2017 Solve each: a) b) c) d) e) f) 7 9.1 complex numbers 2016 ink.notebook On the Worksheet February 21, 2017 Homework Solve. 1. 3. 2. 4. 5. 7. 6. 8. 8 9.1 complex numbers 2016 ink.notebook 9. 10. February 21, 2017 Identify real number parts and imaginary number parts. 13. 3 + 2i 11. 12. Write each expression in radical form. 17. 18. 19. 20. 14. 9 – 3i 15. 4i 16. 6 Write each expression in radical form. 21. 22. 23. 24. 9 9.1 complex numbers 2016 ink.notebook Write each expression in radical form. 25. 26. February 21, 2017 Write each radical in exponential form. 29. 31. 27. 35. 32. 28. Write each radical in exponential form. 33. 30. 34. 35. Write each radical in exponential form. 37. 39. 38. 40. 10 9.1 complex numbers 2016 ink.notebook 41. 45. 42. 46. . February 21, 2017 43. 44. 47. 48. 11 9.1 complex numbers 2016 ink.notebook February 21, 2017 Answers: 12