2.The equation of C3 can be expressed as z=p+qi+ce^iθ, where θ varies from mπ to nπ. What is the value of |n−m|?
2.The equation of C3 can be expressed as z=p+qi+ce^iθ, where θ varies from mπ to nπ. What is the value of |n−m|?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
2.The equation of C3 can be expressed as z=p+qi+ce^iθ, where θ varies from mπ to nπ. What is the value of |n−m|?
![1
f(2) =
(z – 6 + 62) (2 – 1– 1) (z+ 67 – 414)
g(2) = 167 – 16+ 16i
_67
and h (2) = 207 +21.
Also consider the four different paths:
C1: A line segment from (0, 0) to (0, 2) and then another line segment from (0, 2) to (2, 2)
[Coloured blue in the figure].
C2: Straight line from (0,0) to (2,2) [Coloured green in the figure].
C3: A semicircular path from (0,0) to (2, 2) [Coloured red in the figure]. Note that the
dotted semicircle is not a part of the path. Its shown to give a clear idea of the position of the
semicircle C3.
C4: A circle of the form 2 = r, in the anti-clockwise direction, where ris a real number [Not
shown in the figure].
Answer the following questions. Input numerical values up to three decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ce53836-8188-49d8-a49c-7d57b73f59e5%2F23327e3b-042e-4eaf-a840-63fe5b175418%2Frfw8txp_processed.png&w=3840&q=75)
Transcribed Image Text:1
f(2) =
(z – 6 + 62) (2 – 1– 1) (z+ 67 – 414)
g(2) = 167 – 16+ 16i
_67
and h (2) = 207 +21.
Also consider the four different paths:
C1: A line segment from (0, 0) to (0, 2) and then another line segment from (0, 2) to (2, 2)
[Coloured blue in the figure].
C2: Straight line from (0,0) to (2,2) [Coloured green in the figure].
C3: A semicircular path from (0,0) to (2, 2) [Coloured red in the figure]. Note that the
dotted semicircle is not a part of the path. Its shown to give a clear idea of the position of the
semicircle C3.
C4: A circle of the form 2 = r, in the anti-clockwise direction, where ris a real number [Not
shown in the figure].
Answer the following questions. Input numerical values up to three decimal places.
Transcribed Image Text:(2, 2)
(0, 2)
C1
C3
1-
C2
(2, 0)
(0, 0)
-1
3.
1.
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