Section 5 6 Complex Zeros Fundamental Theorem of

Section 5. 6 – Complex Zeros; Fundamental Theorem of Algebra Complex Numbers The complex number system includes real and imaginary numbers. Standard form of a complex number is: a + bi. a and b are real numbers. Fundamental Theorem of Algebra Every complex polynomial function of degree 1 or larger (no negative integers as exponents) has at least one complex zero.

Section 5. 6 – Complex Zeros; Fundamental Theorem of Algebra Theorem Every complex polynomial function of degree n 1 has exactly n complex zeros, some of which may repeat. Conjugate Pairs Theorem Examples 1) A polynomial function of degree three has 2 and 3 + i as it zeros. What is the other zero?

Section 5. 6 – Complex Zeros; Fundamental Theorem of Algebra Examples 2) A polynomial function of degree 5 has 4, 2 + 3 i, and 5 i as it zeros. What are the other zeros? 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?

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?

Section 5. 6 – Complex Zeros; Fundamental Theorem of Algebra Find the remaining complex zeros of the given polynomial functions

Section 5. 6 – Complex Zeros; Fundamental Theorem of Algebra Long Division

Section 5. 6 – Complex Zeros; Fundamental Theorem of Algebra Find the complex zeros of the given polynomial functions

Section 5. 6 – Complex Zeros; Fundamental Theorem of Algebra

Section 5. 6 – Complex Zeros; Fundamental Theorem of Algebra