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QUESTION Let f(2)= 1 +3:+5 (2²+9) cos(4) (1.1) Find the zeros of cos(4). You may use what is known about the zeros of cos z. (1.2) Evaluate [ƒ(2)dz, where C : |2 - 1] = 1. Write your answer in the form a + ib. (1.3) Evaluate [ƒ(2)dz, where C : |2 - i| = 3. Write your answer in the form a + ib. (1.4) For the integral [ƒ(z)dz, where C : [2] = 4, draw the contour with the singularities. DO NOT EVALUATE THE INTEGRAL, but explain what you would do and quote the theorems you will use. You may use one or all of the following theorems: Cauchy-Goursat Theorem, Cauchy's Integral Formulae and the Deformation Corollaries. You must sketch C in each case. Explain how you have used the zeros of cos() to evaluate the contour integrals. You may use the fact that > 3.

QUESTION Let f(2)= 1 +3:+5 (2²+9) cos(4) (1.1) Find the zeros of cos(4). You may use what is known about the zeros of cos z. (1.2) Evaluate [ƒ(2)dz, where C : |2 - 1] = 1. Write your answer in the form a + ib. (1.3) Evaluate [ƒ(2)dz, where C : |2 - i| = 3. Write your answer in the form a + ib. (1.4) For the integral [ƒ(z)dz, where C : [2] = 4, draw the contour with the singularities. DO NOT EVALUATE THE INTEGRAL, but explain what you would do and quote the theorems you will use. You may use one or all of the following theorems: Cauchy-Goursat Theorem, Cauchy's Integral Formulae and the Deformation Corollaries. You must sketch C in each case. Explain how you have used the zeros of cos() to evaluate the contour integrals. You may use the fact that > 3.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 72E
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QUESTION 1 z²+3z +5 Let f(2)= (2²+9) cos() (1.1) Find the zeros of cos(). You may use what is known about the zeros of cos z. Jo f(z)dz, where C:|z1|= 1. Write your answer in the form a + ib. (1.2) Evaluate •Jose f(z)dz, where C: z-i = 3. Write your answer in the form a + ib. (1.3) Evaluate (1.4) For the integral [ƒ(2)dz, where C : |Z| = 4, draw the contour with the singularities. DO NOT EVALUATE THE INTEGRAL, but explain what you would do and quote the theorems you will use. You may use one or all of the following theorems: Cauchy-Goursat Theorem, Cauchy's Integral Formulae and the Deformation Corollaries. You must sketch C in each case. Explain how you have used the zeros of cos() to evaluate the contour integrals. You may use the fact that > 3.
Transcribed Image Text:QUESTION 1 z²+3z +5 Let f(2)= (2²+9) cos() (1.1) Find the zeros of cos(). You may use what is known about the zeros of cos z. Jo f(z)dz, where C:|z1|= 1. Write your answer in the form a + ib. (1.2) Evaluate •Jose f(z)dz, where C: z-i = 3. Write your answer in the form a + ib. (1.3) Evaluate (1.4) For the integral [ƒ(2)dz, where C : |Z| = 4, draw the contour with the singularities. DO NOT EVALUATE THE INTEGRAL, but explain what you would do and quote the theorems you will use. You may use one or all of the following theorems: Cauchy-Goursat Theorem, Cauchy's Integral Formulae and the Deformation Corollaries. You must sketch C in each case. Explain how you have used the zeros of cos() to evaluate the contour integrals. You may use the fact that > 3.
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