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Math · Advanced Math
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4. Consider the polynomial Qa(x) ar 1. a) Express the complex number e-1 in the form a + bi where a, b e R. b) Prove that all roots of the polynomial Qo are sixth roots of unity, that is, if 13] Q。(a) = 0 then aa_ 1. c) Give the definition of the multiplicity of a polynomial root. d) Are there values of α E C such that the polynomial Qa has a root of multiplicity 1? Justify your answer. e) Find all values of o E C such that the polynomial Qa has a root of multiplicity f) Are there values of a E C such that the polynomial Qa has a root of multiplicity g) Find all complex roots of the polynomial Qao where a,--3.2-. 2. 3? Justify your answer.

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