1. Complex numbers
Algebra II Dr. Guram

2. How do we perform operations with complex numbers?.
Focus Questions
How do we perform operations with complex numbers?.
What is an example of a real- world scenario utilizing complex numbers?

3. Curriculum standards
CLE , , , , ,
- compute with … complex numbers.
Sources: /A/1/
Spring Board Algebra 2 workbook
Larson algebra 2 textbook

4. Real World Examples Utilizing complex numbers
What are examples of ways we utilize factoring in real world situations?
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5. Real World Examples Utilizing complex numbers
Fractals: never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. They are in nature.

6. Academic language Imaginary unit i: 𝑖= −1 so 𝑖 2 =−1.
Complex number: a number 𝑎+𝑏𝑖 where 𝑎 and 𝑏 are real numbers and 𝑖 is the imaginary unit.
Imaginary number: a complex number 𝑎+𝑏𝑖 where 𝑏≠0.

7. Academic language
Complex conjugates: two complex numbers of the form 𝑎+𝑏𝑖 and 𝑎−𝑏𝑖.
Complex plane: a coordinate plane in which each point (a, b) represents a complex number 𝑎+𝑏𝑖. The horizontal axis is the real axis and the vertical axis is the imaginary axis.
Absolute value of a complex number: if z =𝑎+𝑏𝑖 then the absolute value of z, denoted 𝑧 = √( 𝑎 2 + 𝑏 2 ) .

8. Square root of a negative number

9. Solving a Quadratic equation with complex numbers

10. practice examples

11. Complex numbers

12. Complex numbers

13. Practice problems

14. Example #4

15. Example #5

16. Example #6

17. Absolute value of a complex number

18. Example #7

19. How do we perform operations with complex numbers?.
Review
How do we perform operations with complex numbers?.
What is an example of a real-world scenario utilizing complex numbers?

20. define the mathematical terms: complex number, and imaginary number.
Review of terms
define the mathematical terms: complex number, and imaginary number.
Define the mathematical terms: complex conjugate, complex plane, and absolute value of a complex number.

21. Classwork/Homework
- worksheet