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Numbers and Their Application to Math and Science

Homework for Numbers Lesson 15

Perform the following operations with complex numbers: (Show work!! Only use a calculator to check your answer.) Problems 1–5 and 7–11 are 2 points each, whereas problems 6 and 12 are 5 points each.
  1. (3 + 5i) + (8 + 9i) =

     

     

  2. (4.5 + 3i) + (3 - 1.5i) =

     

     

  3. (7 + 13i) - (8 + 2i) =

     

     

  4. (-5 + 3i) - (3 - 8i) =

     

     

  5. (-3i) - (13 + 4i) =

     

     

  6. Graph the answers to the problems 1-5 on the grid at the right.

     

     

     

     

     

     

     

  7. (1 + 2i)(1 - 2i) =

     

  8. (2 - 3i)(-3 + 2i) =

     

  9. (3 + 2i)2 =

     

  10. (6 + 8i) ÷ (1 + 3i) =

     

  11. |(3 + 5i)| =

     

     

  12. Graph the answers to the problems 7-11 on the grid to the right.

     

     

     

     

  13. Assuming the cube roots of 1 are equally space around the unit circle, you know the real one (1), and the two complex ones are complex conjugates of each other; graph them and find approximate values for them.

     

  14. Refine your values for the problem above using the exact trigonometric values in the table on page 3 of numbers lesson 11 and check them on your calculator.

     

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