## Complexity

### Johnny WolfeSanta Rosa District Schools

#### Description

Student will perform mathematical operations on complex numbers

#### Objectives

Understands the relative size of integers, rational numbers, irrational numbers, real numbers and complex numbers.

Understands the structure of the complex number system.

The student selects the appropriate operation to solve problems involving addition, subtraction, multiplication, and division of rational numbers, ratios, proportions, and percents, including the appropriate application of the algebraic order of operations.

Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.

#### Materials

- Overhead transparencies (if examples are to be worked on overhead) for Complexity (see attached file).

- Complexity Examples (see attached file).

- Complexity Worksheet (see attached file).

- Complexity Checklist (see attached file).

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for Complexity Examples (see attached file).

2. Have marking pens (for overhead).

3. Have Complexity Examples (see attached file) prepared and ready to demonstrate to students.

4. Have enough copies of Complexity Worksheet (see attached file) for each student.

5. Have enough copies of Complexity Checklist (see attached file) for each student.

#### Procedures

Prior Knowledge: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals and solving equations. Note: This lesson does not address the following: ratios, proportions and percents; square roots, exponents, and appropriate inverse relationships. This lesson contains a checklist to assist the teacher in determining which students need remediation. The sole purpose of this checklist is to aide the teacher in identifying students that need remediation.

1. Discuss the importance of complex numbers (see # 1 on attached file Complexity Examples). Answer student questions and comments.

2. Discuss the Definition of a Complex Number (see # 2 on attached file Complexity Examples). Answer student questions and comments.

3. Discuss the relationship between a complex number and a real number (see # 3 on attached file Complexity Examples). Answer student questions and comments.

4. Discuss the different parts of a complex number (see # 4 on attached file Complexity Examples). Answer student questions and comments.

5. Discuss graphing a complex number in the coordinate system (see # 5 on attached file Complexity Examples). Answer student questions and comments.

6. Discuss complex numbers and writing them as ordered pairs (see # 6 on attached file Complexity Examples). Answer student questions and comments.

7. Work example 7 (see attached file Complexity Examples). Answer student questions and comments.

8. Discuss mathematical operations on complex numbers (see # 8 on attached file Complexity Examples). Answer student questions and comments.

9. Work example 9 (see attached file Complexity Examples). Answer student questions and comments.

10. Work example 10 (see attached file Complexity Examples). Answer student questions and comments.

11. Work example 11 (see attached file Complexity Examples). Answer student questions and comments.

12. Review addition, subtraction, and multiplication of complex numbers (see # 12 on attached file Complexity Examples). Answer student questions and comments.

13. Work example 13 (see attached file Complexity Examples). Answer student questions and comments.

14. Work example 14 (see attached file Complexity Examples). Answer student questions and comments.

15. Work example 15 (see attached file Complexity Examples). Answer student questions and comments.

16. Work example 16 (see attached file Complexity Examples). Answer student questions and comments.

17. Work example 17 (see attached file Complexity Examples). Answer student questions and comments.

18. Distribute the Complexity Worksheet (see attached file).

19. Distribute the Complexity Checklist (see attached file). Describe what constitutes an “A,” “B,” “C,” “D,” and an “F” in the CHECKLIST.

20. The student will write their response on the worksheet.

21. The teacher will move from student to student observing the students work and lending assistance.

#### Assessments

Student worksheets will be taken up and scored according to “Complexity Checklist”. These scores may be placed in the grade book.

#### Extensions

Draw and label the graph of a complex number on the board. Have the students write the complex number in a + bi form from the graph.