Let C be the boundary of the square with vertices 0, 1, 1+i, and i with counterclockwise orientation. (1) Find a parameterisation for C. (2) Evaluate the integral [fa(z) dz, constant. [fa(z) dz, where fa(z) (3) Find all values of a such that √ fa(z) dz = 0. = x² - y² - - ax and a is a complex (4) Let ao be one of the values found in (3). Can we conclude that fa is analytic inside of C? Explain your answer carefully.
Let C be the boundary of the square with vertices 0, 1, 1+i, and i with counterclockwise orientation. (1) Find a parameterisation for C. (2) Evaluate the integral [fa(z) dz, constant. [fa(z) dz, where fa(z) (3) Find all values of a such that √ fa(z) dz = 0. = x² - y² - - ax and a is a complex (4) Let ao be one of the values found in (3). Can we conclude that fa is analytic inside of C? Explain your answer carefully.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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![Let C be the boundary of the square with vertices 0, 1, 1+ i, and
i with counterclockwise orientation.
(1) Find a parameterisation for C.
(2) Evaluate the integral [fa(z) dz,
constant.
[fa(z) dz, where fa(z)
=
x² - y² -
- ax and a is a complex
(3) Find all values of a such that [ fa(z) dz = 0.
(4) Let ao be one of the values found in (3). Can we conclude that fa is analytic inside
of C? Explain your answer carefully.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a7d82e4-2bf5-4850-ba06-9621bb0bd1d8%2F02286d4e-c8ba-4b3e-b3ec-3ddf7394a9d5%2Fclntuo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let C be the boundary of the square with vertices 0, 1, 1+ i, and
i with counterclockwise orientation.
(1) Find a parameterisation for C.
(2) Evaluate the integral [fa(z) dz,
constant.
[fa(z) dz, where fa(z)
=
x² - y² -
- ax and a is a complex
(3) Find all values of a such that [ fa(z) dz = 0.
(4) Let ao be one of the values found in (3). Can we conclude that fa is analytic inside
of C? Explain your answer carefully.
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