5. Let f(z) = + cos z. Let C be a simple contour (but not closed) from the initial point 22 + i 21 = 1 to the terminal point z2 = -1 and not passing through the singular points of f(z). Evaluate f(2) dz.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Do 5th only
4. (a) Derive the expression of cot-1(2).
(b) Find the principal branch of the multiple valued function log(2z – 1). Specify its branch
cut and branch point(s).
5. Let f(2) = 2 + i
+ cos z. Let C be a simple contour (but not closed) from the initial point
21 = 1 to the terminal point z2 = -1 and not passing through the singular points of f(z).
Evaluate
| f(2) dz.
Transcribed Image Text:4. (a) Derive the expression of cot-1(2). (b) Find the principal branch of the multiple valued function log(2z – 1). Specify its branch cut and branch point(s). 5. Let f(2) = 2 + i + cos z. Let C be a simple contour (but not closed) from the initial point 21 = 1 to the terminal point z2 = -1 and not passing through the singular points of f(z). Evaluate | f(2) dz.
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