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Let f (2) = zi + (z – 4). || Part (a) Integrate the function f (z) along the curve C given by z = t3+it² from z = 1 + lito z = 8+ 4i

Let f (2) = zi + (z – 4). || Part (a) Integrate the function f (z) along the curve C given by z = t3+it² from z = 1 + lito z = 8+ 4i

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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Let f (z) = zi+ (z – 4). Part (a) Integrate the function f (z) along the curve C t3+it? from z =1+ lito given by z z = 8+ 4i Part (b) Integrate the same function along the line from O to 6i, then along the line from 6i to 6 + 6i, then finally along the line from 6 + 6i to 0. Note that you are evaluating the integral on a triangular loop. Part (c) Integrate the function f (z) on the circle that goes through 0, 6i, and 6 + 6i. Are the integrals in Part (b) and Part (c) equal?
Transcribed Image Text:Let f (z) = zi+ (z – 4). Part (a) Integrate the function f (z) along the curve C t3+it? from z =1+ lito given by z z = 8+ 4i Part (b) Integrate the same function along the line from O to 6i, then along the line from 6i to 6 + 6i, then finally along the line from 6 + 6i to 0. Note that you are evaluating the integral on a triangular loop. Part (c) Integrate the function f (z) on the circle that goes through 0, 6i, and 6 + 6i. Are the integrals in Part (b) and Part (c) equal?
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