1. Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra Complex Numbers Standard form of a complex number is: a + bi. Every complex polynomial function of degree 1 or larger (no negative integers as exponents) has at least one complex zero. a and b are real numbers. The complex number system includes real and imaginary numbers. Fundamental Theorem of Algebra

2. Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra Conjugate Pairs Theorem Every complex polynomial function of degree n  1 has exactly n complex zeros, some of which may repeat. 1) A polynomial function of degree three has 2 and 3 + i as it zeros. What is the other zero? Theorem Examples

3. Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra 2) A polynomial function of degree 5 has 4, 2 + 3i, and 5i as it zeros. What are the other zeros? Examples 3) A polynomial function of degree 4 has 2 with a zero multiplicity of 2 and 2 – i as it zeros. What are the zeros?

4. Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra Examples 4) A polynomial function of degree 4 has 2 with a zero multiplicity of 2 and 2 – i as it zeros. What is the function?

5. Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra Find the remaining complex zeros of the given polynomial functions

6. Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra Long Division

7. Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra Find the complex zeros of the given polynomial functions

8. Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra

9. Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra