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30. Roots of Polynomials. Find the roots of the following polynomials, using the complex exponential and...
25 (16 com Find all the complex roots. Write the answer in exponential form. The complex fifth roots of - i. (Simplify your answer. Type an exact answer, using a as needed. Use integers or fractions for any numbers in the expression.) 21 = (Simplify your answer. Type an exact answer, using n as needed. Use integers or fractions for any numbers in the expression.) Z2 = (Simplify your answer. Type an exact answer, using a as needed. Use integers...
for complex variables 1. Find all complex roots of the following cubic equation. Write them in standard form z= a +ib where a and b are numerical values (round to 4 digits after decimal point). (a) 23 + 3z +1 = 0 (b) 223 – 622 + 2z+1 = 0
Find all roots, both real and complex, of the following polynomials. When appropriate, given the multiplicity of the root. 11. 2x3 + - 4x +1 12. 8x4 + 4x3 - 6x2 – 5x - 1 13. 3x3 + 9x2 +2+3 14.24 +223 +222? + 50c - 75 15. Find the amplitude, frequency, and period of the function f (t) = 4 sin(2t + 7).
re: 0 of 1 pt 22 of 5.3.59 Find all the complex roots. Write the answer in exponential form. The complex fourth roots of 5+573 i. zo-1 (Simplify your answer. Type an exact answer, using a as needed. Use integers
Using the complex-n-th roots theorem: 5. (a) Use Theorem 10.5.1: Complex n-th Roots Theorem (CNRT) to com- pute all the 4-th roots of -1/4. (b) Factor the polynomial 4x4 + 1 in C[x]. (c) Factor the polynomial 4x4 +1 in R[x]. (d) Use Rational Roots Theorem to prove that the polynomial 4x4 + 1 has no rational roots. Deduce the factorization of 4x4 + 1 in Q[x].
Find all the complex fifth roots of 248,832. Write roots in rectangular form. If necessary, round to the nearest tenth. Choose the five fifth roots of 248,832 below. O A. 12+0 1,3.7+ 11.4i, -9.7+711,-9.7 -7.11,3,7-11.4i O B. 12+0 1.-3.7+11.41.-9.7+7.11.-9.7-7.113.7-11.41 OC. 0+121,3.7+ 11.4i, -9.7+7.11.-9.7-7.11,3.7 - 11.41 OD. 0+121. - 3.7+11.41,-9.7+7.11.-9.7-7.11,3.7 - 114 i
3.11-For each of the following signals compute the complex exponential Fourier series by using trigonometric identities,and then sketch the amplitude and phase spectra for all values of k (a) x(t)-cos(5t-π/4) (b) x(t) sint+ cos t 756 Chapter & The Series and fourier Translorm 023 4 5 ibi FIGURE Pa P33 3.13 Problems 157 in 0 14 12 3 I) ain FIGURE ,3.3 (antísndj (c) sti)-cos(1-1) + sin(,-%) 3.12. Determine the exponential Fourier series tor the Following periodic signals 3.11-For each...
29. Roots and Factors. For each of the following find the roots of the given equations and sketch the roots in the complex plane: (a) cube roots z3 = 1 (b) square roots z2 = i (c) sixth roots z6 = -64 (d) fifth roots z5 = 32e5Ti/3
Find the cube roots of 125 i. Graph each cube root as a vector the complex plane. Choose the correct cube roots below O A. 5(cos 90° + i sin 90°), 5(cos 210° + i sin 210°), 5(cos 330° + i sin 330%) OB. 5(cos 30° + i sin 30°), 5(cos 150° + i sin 150°), 5(cos 270° + i sin 270º) O C. 125(cos 0° + i sin 0°), 125(cos 120° + i sin 120°), 125(cos 240° + i...
1(a) Find the square roots of the complex number z -3 + j4, expressing your answer in the form a + jb. Hence find the roots for the quadratic equation: x2-x(1- 0 giving your answer in the form p+ q where p is a real number and q is a complex number. I7 marks] (b) Express: 3 + in the form ω-reje (r> 0, 0 which o is real and positive. θ < 2π). Hence find the smallest value of...