(a) Determine all distinct values of vZA given that A = -1+ iv3.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 5E: 5. Prove that the equation has no solution in an ordered integral domain.
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(a)
Determine all distinct values of v2A given that
A = -1+ iv3.
(b) Given
f(2) = z? – 3ixy.
(i)
Determine whether f(z) is an analytic function or not.
(ii)
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).
1
Figure 1 Curves a and B.
3.
Transcribed Image Text:(a) Determine all distinct values of v2A given that A = -1+ iv3. (b) Given f(2) = z? – 3ixy. (i) Determine whether f(z) is an analytic function or not. (ii) 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). 1 Figure 1 Curves a and B. 3.
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