Stitz-Zeager_College_Algebra_e-book

Theorem 584 bisection method 215 cartesian coordinate

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Unformatted text preview: 4 3 √ √ √ 3. Let z = − 3 2 3 + 3 i and w = 3 2 − 3i 2. Compute the following. Express your answers in 2 polar form using the principal argument. (a) zw (b) (c) z w (d) w z z4 (e) w3 (f) z 5 w2 4. Find the following complex roots. Express your answers in polar using the principal argument and then convert them into rectangular form. (a) the three cube roots of z = i (b) the six sixth roots of z = 64 (c) the two square roots of 5 2 − √ 53 2i 5. Use the Sum and Difference Identities in Theorem 10.16 or √ Half Angle Identities in the √ Theorem 10.19 to express the three cube roots of z = 2 + i 2 in rectangular form. (See Example 11.7.4, number 3.) 6. Use a calculator to approximate the five fifth roots of 1. (See Example 11.7.4, number 4.) 7. According to Theorem 3.16 in Section 3.4, the polynomial p(x) = x4 + 4 can be factored into the product linear and irreducible quadratic factors. In Exercise 13 in Section 8.7, we showed you how to factor this polynomial into the product of two irreducible quadratic factors using a system of non-linear equations. Now that we can compute the complex fourth roots of −4 directly, we can simply apply the Complex Factorization Theorem, Theorem 3.14, to obtain the linear factorization p(x) = (x − (1 + i))(x − (1 − i))(x − (−1 + i))(x − (−1 − i)). By multiplying the...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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