complex variables Question 9 Use the residue theory to evaluate
evaluate the definite integral in the complex plane by using residue theorem 27 LCos (ne-sn) de, no hnt: Cose 2+2 27 LCos (ne-sn) de, no hnt: Cose 2+2
4. [10 marks] Follow the method we did for J dr, use the residue theorem to compute the following integral using the complex plane: da:
5. Use Cauchy's residue theorem to evaluate the following integrals along the circle 121 = 4: C 22 5. Use Cauchy's residue theorem to evaluate the following integrals along the circle 121 = 4: C 22
Compute the following using the residue theorem (complex analysis):
solve a and c only 1. Use the residue theorem to evaluate the following integrals: cos θ (2+sin θ) 2n 0 0 1+sin2 θ 2x-0820, de (C) Jo 5-4cos
Problem 1: (10 pts) Let Y(S) = 4:0251712s+10 Use Matlab's "tf2zpk" and "residue" commands to: k (s-- (-2) a) (5 pts) Convert y(s) into pole-zero form, 1.e -p -p,Xs-p.)(-p) "polei zero are com en If pole/zero are complex, combine conjugate pairs into 2nd order terms with real coefficients. b) (5 pts) Find the inverse Laplace transform y(t). Please combine conjugate complex parts so that y(t) is real (not complex).
use residue theorem to evaluate the following integrals 16) cosa 30 de 5- 4 cos 20 17) COSI det (x + 1)? sin 3x dx 18) sin x dx (x² + 4x+5 19)
using Cauchy's Residue Theorem and the so-alled pacman inte 6. (10 pts) Evaluate gration contour. using Cauchy's Residue Theorem and the so-alled pacman inte 6. (10 pts) Evaluate gration contour.
use residue theorem to evaluate the following integrals sin z 21) 20) Cosx dx (r? + 1) X 22) sin mx dx 2(x² + a²² (a > 0, b>0) 23) cos ex - cos bx -dx x?