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Unlocking Complex Zeros: Fundamental Theorem of Algebra Examples and Solutions" (59 characters)

Explore the complex number system, polynomial functions, conjugate pairs theorem, and find complex zeros. Examples provided for better understanding. Discover how to find remaining complex zeros using long division.

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Unlocking Complex Zeros: Fundamental Theorem of Algebra Examples and Solutions" (59 characters)

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  1. 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. • i is the imaginary unit ( Fundamental Theorem of Algebra Every complex polynomial function of degree 1 or larger (no negative integers as exponents) has at least one complex zero.

  2. 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 • If is a zero of a polynomial function whose coefficients are real numbers, then the complex conjugate is also a zero of the function. Examples • 1) A polynomial function of degree three has 2 and 3 + i as it zeros. What is the other zero?

  3. Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra Examples • 2) A polynomial function of degree 5 has 4, 2 + 3i, and 5i 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?

  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 5)

  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 6) Possible solutions: Try: Try:

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

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

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