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This 4 page Class Notes was uploaded by Rebecca Favorit on Friday March 6, 2015. The Class Notes belongs to 106-06 at Washington State University taught by mindy morgan in Spring2015. Since its upload, it has received 79 views. For similar materials see College Algebra in Math at Washington State University.
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Date Created: 03/06/15
Math 10606 Notes for March 2nd 4th and 6th March 2 2015 Announcements aAssessment 2 on Wednesday 34 bEampN 24 due Friday 36 c Exam 2 Wednesday 311 from 6715pm a Abelson 201 dReview Session a Tuesday 310 from 68pm Abelson 201 Section 23 Complex Numbers Complex Number 0 Zabi o A is the quotreal part 0 B without the i is the quotimaginary part 0 I is the imaginary number 0 square root of 1 Complex Plane 0 Horizontal axis real axis 0 Vertical axis imaginary axis 0 Abi9ab Modulus 0 Measures the size of z o It is the distance between the origin and the plotted complex number Mulptiplying HI 0 When FOLing a problem if there is a value that has an to the 2Incl power you would substitute a 1 into the problem 0 Note when there are radicals you always want to have the radical at the end of your final answer I Example 0 6i2 Square Root Symbol March 4 2015 Section 24 Complex Roots of Polynomials Fundamental Theorem of Algebra 0 Complex roots are in the form zabi o Pureimaginary number 0 ZObi Which would equal bi March 6 2015 Announcements Hw 15 due Thursday 31212 o It has material that will be covered on Exam 2 so try to work through it before the exam Section 24 Continued Theorem 0 If fx is a polynomial function and if zabi is a root of fx then wabi is also a root 0 So abi and abi are complex conjegates Theorem 2 o Nth degree polynomials will have exactly n complex roots counting multiplicities Theorem 3 o Nth degree polynomials can be written in root form as a product of n linear factors Irreducible Quadratics o It is in the form fx axquot2bxc with no rational roots 0 Example 25xquot220x13 I It is an irreducible quadratic because you cannot reduce the factors Theorem 4 o Nquotn degree polynomials can be written as the product of linear and irreducible quadratic factors 0 You can use any of the techniques to solve any of the problems and simplify them more until they cannot be simplified anymore