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f(z) = z² – 3ixy. (1) Determine whether f (z) is an analytic function or not. Evaluate the line integral of f(z) from z = 1 to z = i along the curves a and ß, where a follows the axes and passes through the origin, while ß is an anticlockwise arc of a unit circle centred at the origin (see Figure 1 below). (ii) 1 a 1 Figure 1 Curves a and ß.

f(z) = z² – 3ixy. (1) Determine whether f (z) is an analytic function or not. Evaluate the line integral of f(z) from z = 1 to z = i along the curves a and ß, where a follows the axes and passes through the origin, while ß is an anticlockwise arc of a unit circle centred at the origin (see Figure 1 below). (ii) 1 a 1 Figure 1 Curves a and ß.

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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(b) Given f(z) = z? – 3ixy. (1) Determine whether f(z) is an analytic function or not. Evaluate the line integral of f(z) from z = 1 to z = i along the curves a and ß, where a follows the axes and passes through the origin, while B is an anticlockwise arc of a unit circle centred at the origin (see Figure 1 below). (ii) y 1 1 Figure 1 Curves a and ß.
Transcribed Image Text:(b) Given f(z) = z? – 3ixy. (1) Determine whether f(z) is an analytic function or not. Evaluate the line integral of f(z) from z = 1 to z = i along the curves a and ß, where a follows the axes and passes through the origin, while B is an anticlockwise arc of a unit circle centred at the origin (see Figure 1 below). (ii) y 1 1 Figure 1 Curves a and ß.
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