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Zill & Shanahan - Complex Analysis 3/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 12 / 17

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7 8 9 10
2/2 1/2 1/1 3/3 0/1 0/1 1/1 –/1 1/2 3/3
Total
12/17 (70.6%)

  • Instructions

    Complex Analysis: A First Course with Applications, by Dennis G. Zill and Patrick D. Shanahan, is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex analysis, this text discusses the theory of the most relevant mathematical topics in a student-friendly manner. The WebAssign component provides students with instant question feedback and links to the appropriate section of an eBook.

    Question 1 uses special grading to check that the complex number is written in both the correct polar form and correct a + bi form, respectively.

    Question 2 uses list grading that lets a student enter all the roots in one blank.

    Question 3 uses differential equation grading to test the validity of the answer. This question accepts any correct form of the answer and runs student responses through a series of tests to ensure the assumptions and requirements of the question are met.

    Question 4 asks a student to find an image in terms of u and v. The question allows the student to enter any mathematically equivalent version of the question.

    Question 5 utilizes special grading so a student can enter the arbitrary solutions as a comma-separated list of answers.

    Question 7 illustrates vector grading.

    Question 9 uses series grading, which allows any correct version of the series based on the summation index. It also includes an answer of INFINITY. For R, try entering both INFINITY and ∞. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 2/2 points  |  Previous Answers ZillCAnalysis3 1.3.025. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
2/50 2/50
Total
2/2
 
Use
zn = rn(cos(nθ) + i sin(nθ))
 to compute the indicated power. Write the complex number in polar form.
(1 + 
3
i)12
4096(cos(0)+isin(0))
Correct: Your answer is correct. webMathematica generated answer key
Write the complex number in the form
a + ib.
4096
Correct: Your answer is correct. webMathematica generated answer key
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2. 1/2 points  |  Previous Answers ZillCAnalysis3 1.4.001. My Notes
Question Part
Points
Submissions Used
1 2
0/1 1/1
2/50 1/50
Total
1/2
 
Use
wk = 
nr
cos
θ + 2kπ
n
 + i sin
θ + 2kπ
n
to compute all roots. Give the principal nth root in each case.
(8)1/3
Incorrect: Your answer is incorrect. webMathematica generated answer key
Sketch the roots
w0, w1,   , wn − 1
 on an appropriate circle centered at the origin.

Correct: Your answer is correct.
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3. 1/1 points  |  Previous Answers ZillCAnalysis3 1.6.013. My Notes
Question Part
Points
Submissions Used
1
1/1
2/50
Total
1/1
 
Find the general solution of the given homogeneous differential equation.
y'' − 8y' + 80y = 0
y(x) =
e4x(c1​cos(8x)+c2​sin(8x))
Correct: Your answer is correct. webMathematica generated answer key
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4. 3/3 points  |  Previous Answers ZillCAnalysis3 2.4.003. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
2/50 2/50 2/50
Total
3/3
 
Find the image of the given set under the mapping
w = z2.
 (Give your answer in terms of u and v.)
the line
x = 2
u=4−(v2)16​
Correct: Your answer is correct. webMathematica generated answer key
Represent the mapping by drawing the set.

Correct: Your answer is correct.
Represent the mapping by drawing its image.

Correct: Your answer is correct.
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5. 0/1 points  |  Previous Answers ZillCAnalysis3 4.3.026. My Notes
Question Part
Points
Submissions Used
1
0/1
1/50
Total
0/1
 
Find all complex values z satisfying the given equation. (Enter your answers as a comma-separated list.)
sinh(z) = −1
z =
sinh−1(−1)
Incorrect: Your answer is incorrect. webMathematica generated answer key ,    n = 0, ±1, ±2,   
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6. 0/1 points  |  Previous Answers ZillCAnalysis3 5.5.021. My Notes
Question Part
Points
Submissions Used
1
0/1
1/50
Total
0/1
 
Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to evaluate the given integral along the indicated closed contour(s). (Write your answer in the form
a + ib.)
 
C
1
z3(z − 1)2
 dz; |z − 3| = 4
23
Incorrect: Your answer is incorrect. webMathematica generated answer key
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7. 1/1 points  |  Previous Answers ZillCAnalysis3 5.6.010. My Notes
Question Part
Points
Submissions Used
1
1/1
2/50
Total
1/1
 
Find the velocity field
F(x, y)
 of the flow of an ideal fluid determined by the given analytic function
g(z).
g(z) = sin(z)
F(x, y) =
⟨sin(x)cosh(y),−cos(x)sinh(y)⟩
Correct: Your answer is correct. webMathematica generated answer key
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8. –/1 points ZillCAnalysis3 5.6.013. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
Find a complex velocity potential
Ω(z)
 of the complex representation
f(z)
 of the indicated velocity field
F(x, y).
 Verify your answer using
f(z) = Ω'(z).
F(x, y) = (cos(θ0))i + (sin(θ0))j,
θ0
 a constant
Ω(z) =
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9. 1/2 points  |  Previous Answers ZillCAnalysis3 6.2.010. My Notes
Question Part
Points
Submissions Used
1 2
0/1 1/1
1/50 1/50
Total
1/2
 
Use known results to expand the given function in a Maclaurin series.
f(z) = sin(3z)
∞
k = 0
12
Incorrect: Your answer is incorrect. webMathematica generated answer key
Give the radius of convergence R of the series.
R =
∞
Correct: Your answer is correct. webMathematica generated answer key
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10. 3/3 points  |  Previous Answers ZillCAnalysis3 6.R.038. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
1/50 1/50 1/50
Total
3/3
 
Try to fill in the blanks without referring back to the text.
On
|z| = 1,
 the contour integral
 
C
cos(z)
z2 − (2 + π)z + 2π
 dz
 equals
0
Correct: Your answer is correct. webMathematica generated answer key , on
|z| = 3
 the integral equals
2πicos(2)2−π​
Correct: Your answer is correct. webMathematica generated answer key , and on
|z| = 4
 the integral equals
2πi(cos(2)+12−π​)
Correct: Your answer is correct. webMathematica generated answer key .
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