THIS QUESTION CONTAINS PARTS (a), (b), (c). PLEASE SCROLL DOWN AND ATTEMPT ALL PARTS. O Consider the linear fractional transformation HINT: you should not need to do any major algebraic calculations for this question. (b) Find the image of the set (a) Evaluate in the extended complex plane T(0) and T(-5i) and T (oo). Enter your answers in the boxes below as exact values (do not use decimals) in correct Maple notation, for example, 95-54*I, using a capital I. If any of your answers is oo, enter the word INFINITY in capital letters. Answers: T(0) = O ?currPage=1&testid-29660&actionID=next T: CC where T(z) = 团团 the image is the exterior of a circle the image is bounded by a line, and the image contains the poiht w=0 O the image is bounded by a line, and the image does not contain the point w=0 O {z C | Re(z) <0} under the transformation w = T(z), and draw a carefully labelled sketch of the image. (You do not have to submit your sketch.) Which of the following describes the image? O the image is the interior of a circle -5 (-1-91)z-51 B.T(-5i) 33 Submit Assignment Game B.T()= Quit & Save A O Back Question Menu - Next ENG 1:36 PM 10/11/2022 易
THIS QUESTION CONTAINS PARTS (a), (b), (c). PLEASE SCROLL DOWN AND ATTEMPT ALL PARTS. O Consider the linear fractional transformation HINT: you should not need to do any major algebraic calculations for this question. (b) Find the image of the set (a) Evaluate in the extended complex plane T(0) and T(-5i) and T (oo). Enter your answers in the boxes below as exact values (do not use decimals) in correct Maple notation, for example, 95-54*I, using a capital I. If any of your answers is oo, enter the word INFINITY in capital letters. Answers: T(0) = O ?currPage=1&testid-29660&actionID=next T: CC where T(z) = 团团 the image is the exterior of a circle the image is bounded by a line, and the image contains the poiht w=0 O the image is bounded by a line, and the image does not contain the point w=0 O {z C | Re(z) <0} under the transformation w = T(z), and draw a carefully labelled sketch of the image. (You do not have to submit your sketch.) Which of the following describes the image? O the image is the interior of a circle -5 (-1-91)z-51 B.T(-5i) 33 Submit Assignment Game B.T()= Quit & Save A O Back Question Menu - Next ENG 1:36 PM 10/11/2022 易
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 41E
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![word INFINITY in capital letters.
Answers: T(0) =
(b) Find the image of the set
30
T(-5i) =
{ze C* | Re(z) <0}
under the transformation w = T(z), and draw a carefully labelled sketch of the image. (You do not have to submit your sketch.)
Which of the following describes the image?
O the image is the interior of a circle
O
the image is the exterior of a circle
O
the image is bounded by a line, and the image contains the point w=0
O the image is bounded by a line, and the image does not contain the point w=0
(c) If your answer to part (b) involved a circle, find the centre and radius of the circle; if it involved a line, find two points on the line.
Carefully follow the instructions and enter your answer in the box below.
Answer:
.T(x) =
• For a circle: enter the centre as a complex number, followed by a comma, followed by the radius, all enclosed in square
brackets. Example: if the centre is 4-5i and the radius is √6 you should type [4-5*1, sqrt (6)], Always use exact
values, do not enter decimals.
. For a line: enter two points as complex numbers, separated by a comma, all enclosed in square brackets. The order of the
points in your answer does not matter. Example: if your two points are 7 + 8i and -9i, you should type [7+8*1, -9*1] or
[-9*1, 7+8*1]. Always use exact values, do not enter decimals.
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Transcribed Image Text:word INFINITY in capital letters.
Answers: T(0) =
(b) Find the image of the set
30
T(-5i) =
{ze C* | Re(z) <0}
under the transformation w = T(z), and draw a carefully labelled sketch of the image. (You do not have to submit your sketch.)
Which of the following describes the image?
O the image is the interior of a circle
O
the image is the exterior of a circle
O
the image is bounded by a line, and the image contains the point w=0
O the image is bounded by a line, and the image does not contain the point w=0
(c) If your answer to part (b) involved a circle, find the centre and radius of the circle; if it involved a line, find two points on the line.
Carefully follow the instructions and enter your answer in the box below.
Answer:
.T(x) =
• For a circle: enter the centre as a complex number, followed by a comma, followed by the radius, all enclosed in square
brackets. Example: if the centre is 4-5i and the radius is √6 you should type [4-5*1, sqrt (6)], Always use exact
values, do not enter decimals.
. For a line: enter two points as complex numbers, separated by a comma, all enclosed in square brackets. The order of the
points in your answer does not matter. Example: if your two points are 7 + 8i and -9i, you should type [7+8*1, -9*1] or
[-9*1, 7+8*1]. Always use exact values, do not enter decimals.
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Transcribed Image Text:2
O
THIS QUESTION CONTAINS PARTS (a), (b), (c). PLEASE SCROLL DOWN AND ATTEMPT ALL PARTS.
E
Consider the linear fractional transformation
(b) Find the image of the set
HINT: you should not need to do any major algebraic calculations for this question.
(a) Evaluate in the extended complex plane T(0) and T(-5i) and T (oo). Enter your answers in the boxes below as exact values
(do not use decimals) in correct Maple notation, for example, 95-54*I, using a capital I. If any of your answers is oo, enter the
word INFINITY in capital letters.
Answers: T(0)
red Test.QuestionSheet?currPage=1&testid-29660&actionID=next
OOC
T: CC where T(2)
26.
B.T(-5)
-5
(-1-91)z-5i
{z EC | Re(z) <0}
under the transformation w = T(z), and draw a carefully labelled sketch of the image. (You do not have to submit your sketch.)
Which of the following describes the image?
O the image is the interior of a circle
the image is the exterior of a circle
the image is bounded by a line, and the image contains the poiht w=0
O the image is bounded by a line, and the image does not contain the point w=0
G
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B7(0) =
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1:36 PM
10/11/2022
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