1. 4.8 Complex Numbers Learning goals
identify, graph, and perform operations with complex numbers
find complex number solutions of quadratic equations

2. Vocabulary complex number: a + bi a is the real number part
bi is the imaginary number part
If b is 0, then a is a real number; if a is 0, then bi is a pure imaginary number

3. imaginary number (i)

4. Ex 1

5. Ex 2
Write in a + bi form

6. Ex 3

7. Ex 4

8. Imaginary numbers pattern
MEMORIZE!!!!!!

9. Ex 5

10. Ex 6
Solve

11. Complex Conjugates
Complex conjugates are used to rationalize complex binomials found in the denominator
The product of complex conjugates is a REAL number
Why can’t there be an i in the denominator of a fraction?

12. Ex 7
Simplify

13. Ex 8
Simplify

14. Think about it…
Explain the difference between the additive inverse of a complex number and complex conjugate.