3. Consider the integral sinh 3z dz. Jc z? – 7iz – 10 Determine the point(s) at which the integrand is non-analytic and hence, using Cauchy's integral formula/theorem, evaluate the integral when a. C = C1, where C, is an anticlockwise circle of radius 3 centred at the origin. b. C = C2, where C2 is an anticlockwise circle of radius 3 centred at z = 3i. In doing the integrations, provide a sketch of the relevant curve(s) and point(s) of non-analyticity. [You may find it useful to recall that sinh iz = i sin z.]
3. Consider the integral sinh 3z dz. Jc z? – 7iz – 10 Determine the point(s) at which the integrand is non-analytic and hence, using Cauchy's integral formula/theorem, evaluate the integral when a. C = C1, where C, is an anticlockwise circle of radius 3 centred at the origin. b. C = C2, where C2 is an anticlockwise circle of radius 3 centred at z = 3i. In doing the integrations, provide a sketch of the relevant curve(s) and point(s) of non-analyticity. [You may find it useful to recall that sinh iz = i sin z.]
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 15CM
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![3. Consider the integral
sinh 3z
dz.
Jc z? – 7iz – 10
Determine the point(s) at which the integrand is non-analytic and hence, using Cauchy's integral
formula/theorem, evaluate the integral when
a. C = C1, where C, is an anticlockwise circle of radius 3 centred at the origin.
b. C = C2, where C2 is an anticlockwise circle of radius 3 centred at z = 3i.
In doing the integrations, provide a sketch of the relevant curve(s) and point(s) of non-analyticity.
[You may find it useful to recall that sinh iz = i sin z.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb665f96-8ef0-4ccd-80eb-2aa2625dc822%2Fd7d662fa-fc71-4087-a9d2-ac6a83a37ea5%2F386co9j_processed.png&w=3840&q=75)
Transcribed Image Text:3. Consider the integral
sinh 3z
dz.
Jc z? – 7iz – 10
Determine the point(s) at which the integrand is non-analytic and hence, using Cauchy's integral
formula/theorem, evaluate the integral when
a. C = C1, where C, is an anticlockwise circle of radius 3 centred at the origin.
b. C = C2, where C2 is an anticlockwise circle of radius 3 centred at z = 3i.
In doing the integrations, provide a sketch of the relevant curve(s) and point(s) of non-analyticity.
[You may find it useful to recall that sinh iz = i sin z.]
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