Math 142: Unit 7

Deadline: Thursday August 15

Topics
The Analytic Geometry section of the course begins with this unit, which consists of two parts. The first is an introduction to polar coordinates for points in the xy-plane. The second is a study of complex numbers. The two topics are related by the polar form of a complex number, which then leads to simple formulas for finding powers and roots of complex number via DeMoivre's Theorem.

• Polar Coordinates (7.5)
  • Converting from rectangular to polar coordinates.
  • Converting from polar to rectangular coordinates.
  • Equations in polar coordinates.
  • Graphs of functions and relations given in polar coordinates.
• Complex numbers (1.5 and 7.6)
  • definition
  • addition and subtraction
  • multiplication
  • division
  • polar form
• DeMoivre's Theorem (7.7)
  • powers of complex numbers
  • roots of complex numbers

Study guideline

• Section 7.5: Polar Coordinates
  • Reading: pages 541-553.
    Read and work through examples 1-8 and their associated matched problems.
    Read and respond to "Explore and Discuss" 1.
  • Problems: pages 553-555 #1, 3, 5, 7, 11, 13, 15, 17-28, 29, 31, 33, 39, 41, 43, 45-56, 59, 63, 65
    • More practice problems, with solutions
      
      
• Section 1.5 (review): Complex Numbers
  • Reading: section 1.5
    Concepts you should know:
    • definition of complex numbers
    • addition and substraction of complex numbers
    • multiplication of complex numbers
    • division of complex numbers
  • Problems: Work through a representative sampling of the problems in this section until you feel comfortable with the material.
    • More practice problems, with solutions
      
      
• Section 7.6: Complex Numbers in Rectangular and Polar Form
  • Reading: pages 555-562.
    Read and work through examples 1-4 and their associated matched problems.
    Read and respond to "Explore and Discuss" 1, 2, and 3.
  • Problems: pages 562-563 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27
    • More practice problems, with solutions
      
      
• Section 7.7: DeMoivre's Theorem
  • Reading: pages 563-567.
    Read and work through examples 1-3.
  • Problems: pages 568-569 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25-31, 33, 35, 37, 41, 43, 45
    • More practice problems, with solutions
      
      
• Supplementary material (optional) for sections 7.5-7
  • Schaum's Precalculus Outline, parts of chapter 28 and 29
  • Additional application #5 for chapter 7, with answer
  • Additional exercises and demonstrations provided by other websites, for chapter 7.
  • Answers to review problems from the textbook.
  • Calculator key stroke guides
  • The CD-ROM that came with your textbook has tutorials, practice exams, and interesting "Interactive Diagrams".
  • Browse through the Archive Center on the NetTutor web site. Detailed solutions to selected problems are saved in the Archive Center.

Unit Exam #7
After completing the above work, do the following:

1. Read the exam description:
   • This exam has 20 questions, and will count 20 points toward your grade. 
   • This exam has a one hour time limit.
   • All questions on this exam require an exact answer. You should not try to use a calculator approximation for any of these questions.
   • Type the letter i for the square root of -1, and the letter e for the number e. Be careful to put in all necessary parentheses when typing your answer, especially for problems in polar form. For example, 1+i in polar form would be entered as sqrt(2)*e^(pi*i/4) or sqrt(2)*e^((pi*i)/4). Make sure you use the preview button to prevent any mistakes! (The second form above looks better in the preview, but both are correct.)
   • Be sure to look under the entry box for the type of answer expected.
     • Some problems expect a list of several values or formulas separated by semicolons, such as 0;5pi/6;7pi/6. In this case, the order of the values is not important.
     • The answer to some problems is an equation (for example, the equation of a line). In this case, simply type in the equation. For example, your answer might be y=2x-3 or r=cos(t).
   • Make sure your calculator is set to the correct mode (radians or degrees) for each problem.
   • For this exam, you must know how to graph curves in polar coordinates using your calculator.
   • This exam may be somewhat easier if you know how to work with complex numbers on your calculator. However, remember that you should not use approximations -- all questions on this exam require an exact answer.
   • In previous classes, students had the most difficulty with (a) finding roots of complex numbers and (b) converting from rectangular to polar coordinates (or rectangular to polar form of a complex number).
2. Complete the online Unit 7 Pretest assignment for Math 142. You may use your book if you wish, and redo the pretest as many times as you like. Your pretest score will be scaled to 5 points maximum.
   • Directions: Click on the link above for your class, then choose the Unit 7 Pretest.
   • The pretest must be completed by the deadline date listed at the top of this page.
     However, you may redo the pretest as many times as you like before the due date.
     Your best score counts, and it will be rescaled to 5 points maximum.
3. If you are having trouble with any of the problems listed above or on the pretest or practice exams, make use of the help resources listed on the Help page.
4. Arrange with your proctor to take the online proctored Unit 7 Exam assignment for Math 142. Remember to bring identification, and remember that you will not be able to take the unit exam after the deadline date given at the top of this page. You may NOT use your book or notes on this exam.
   • Directions: Click on the link above for your class, then choose Unit 7 Exam.
   • The proctored unit exam must be completed by the deadline date listed at the top of this page, and may be repeated under certain conditions. See the Detailed Schedule page for Math 142 for specific rules.

   Note: Remember that you can always go back and take practice exams on this unit for Math 142 after the deadline has passed. In particular, this will help you prepare for the midterm and final exams.

   • Directions: Click on the link above for your class, then choose Unit 7 Exam. After the deadline has passed, this exam will be available in practice mode.

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