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(b) Let C₂ be the contour from 10 + 10 i to 5/8 which consists of an anticlockwise arc of the circle with centre 0 and radius 5√/8. Then C₂ can be parametrised as follows (select all correct answers): Oz=2+√√200-22 for z from 10 to 5/8 " □=5/8e for 0 from 0 to 4 D5/B for 0 from 0 to 2m D-5√80 for from to 0 4 □ (10+104)+(5/8-10-10%) for t from 0 to 1 05/8 (cos@+isin) for 8 from 4 D == 5/8e (10+10)t fort from 1 to 0 Now evaluate the integral along C₂ of f(=), and enter your answer in the box. √₂ Answer: to 0 f(2) dz 63

(b) Let C₂ be the contour from 10 + 10 i to 5/8 which consists of an anticlockwise arc of the circle with centre 0 and radius 5√/8. Then C₂ can be parametrised as follows (select all correct answers): Oz=2+√√200-22 for z from 10 to 5/8 " □=5/8e for 0 from 0 to 4 D5/B for 0 from 0 to 2m D-5√80 for from to 0 4 □ (10+104)+(5/8-10-10%) for t from 0 to 1 05/8 (cos@+isin) for 8 from 4 D == 5/8e (10+10)t fort from 1 to 0 Now evaluate the integral along C₂ of f(=), and enter your answer in the box. √₂ Answer: to 0 f(2) dz 63

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Part B needed Kindly solve part B in 10 minutes
Let In the current question we'll evaluate the integral of f(z) along two separate curves by using the method of parametrisation. Your evaluations must be given as complex numbers in correct Maple syntax. You may use a capital I for the complex number i, and Pi (with a capital P) for . You may use 1n for the natural logarithm of a positive real number, and you may use the exponential, trigonometric and hyperbolic functions: for example, ln (21) and exp (Pi*1/22) and cos (23) and arctan (24/25). O==t(2+2i) for t from 1 to 5 Oz=x+iz for z from 2 to 10 Oz=a+t(B-a) for t from 0 to 1 Oz (10 + 10i) +t(8+8i) for t from 0 to 1 Oy=zfor æ from 2 to 10 0 z from 2+2i to 10+10i Oz= (2+2i)ei for 0 from 1 to 5 Oz (2+2)+1(8+81) for t from 0 to 1 f(z) = (a) Let C₁ be the straight line segment from 2 + 2 i to 10+10i. Then C₁ can be parametrised as follows (select all correct answers): Arg(z) Answer: Now evaluate the integral along C₁ of f(z), and enter your answer in the box. Jo f(z) dz=
Transcribed Image Text:Let In the current question we'll evaluate the integral of f(z) along two separate curves by using the method of parametrisation. Your evaluations must be given as complex numbers in correct Maple syntax. You may use a capital I for the complex number i, and Pi (with a capital P) for . You may use 1n for the natural logarithm of a positive real number, and you may use the exponential, trigonometric and hyperbolic functions: for example, ln (21) and exp (Pi*1/22) and cos (23) and arctan (24/25). O==t(2+2i) for t from 1 to 5 Oz=x+iz for z from 2 to 10 Oz=a+t(B-a) for t from 0 to 1 Oz (10 + 10i) +t(8+8i) for t from 0 to 1 Oy=zfor æ from 2 to 10 0 z from 2+2i to 10+10i Oz= (2+2i)ei for 0 from 1 to 5 Oz (2+2)+1(8+81) for t from 0 to 1 f(z) = (a) Let C₁ be the straight line segment from 2 + 2 i to 10+10i. Then C₁ can be parametrised as follows (select all correct answers): Arg(z) Answer: Now evaluate the integral along C₁ of f(z), and enter your answer in the box. Jo f(z) dz=
(b) Let C₂ be the contour from 10 + 10 i to 5/8 which consists of an anticlockwise arc of the circle with centre 0 and radius 5√/8. Then C₂ can be parametrised as follows (select all correct answers): O z=z+i√/200-22 for z from 10 to 5/8 # □ z=5√810 for 0 from 0 to 4 Oz-5/8e0 for @ from 0 to 2 D=5√8e for @ from to 0 Oz (10+10) +t(5/8-10-10%) for t from 0 to 1 D=5√8 (cos@+isin) for @ from to 0 4 Oz 5/8e(10+10i)t for t from 1 to 0 Now evaluate the integral along C₂ of f(z), and enter your answer in the box. √₂1(2) dz 20 Answer: M Submit Assignment 23°C Quit & Save OP d Back Question Menu ENG 2:51 PM 10/11/2022 見
Transcribed Image Text:(b) Let C₂ be the contour from 10 + 10 i to 5/8 which consists of an anticlockwise arc of the circle with centre 0 and radius 5√/8. Then C₂ can be parametrised as follows (select all correct answers): O z=z+i√/200-22 for z from 10 to 5/8 # □ z=5√810 for 0 from 0 to 4 Oz-5/8e0 for @ from 0 to 2 D=5√8e for @ from to 0 Oz (10+10) +t(5/8-10-10%) for t from 0 to 1 D=5√8 (cos@+isin) for @ from to 0 4 Oz 5/8e(10+10i)t for t from 1 to 0 Now evaluate the integral along C₂ of f(z), and enter your answer in the box. √₂1(2) dz 20 Answer: M Submit Assignment 23°C Quit & Save OP d Back Question Menu ENG 2:51 PM 10/11/2022 見
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