On this webpage you will find my solutions to the eighth edition of "Complex Variables and Applications" by Ruel V. Churchill and James W. Brown. Here is a link to the book's page on amazon.com. If you find my work useful, please consider making a donation. Thank you.


Chapter 1 - Complex Numbers
Section 2 Section 3 Section 4 Section 5 Section 8 Section 10 Section 11
Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7
Exercise 8 Exercise 8 Exercise 8 Exercise 8 Exercise 8 Exercise 8
Exercise 9 Exercise 9 Exercise 9 Exercise 9 Exercise 9
Exercise 10 Exercise 10 Exercise 10 Exercise 10
Exercise 11 Exercise 11 Exercise 11
Exercise 12
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Chapter 2 - Analytic Functions
Section 12 Section 14 Section 18 Section 20
Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7 Exercise 7
Exercise 8 Exercise 8 Exercise 8
Exercise 9 Exercise 9
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Chapter 2 - Analytic Functions
Section 23 Section 25 Section 26 Section 28
Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7 Exercise 7
Exercise 8 Exercise 8
Exercise 9 Exercise 9
Exercise 10 Exercise 10
Exercise 11
Chapter 3 - Elementary Functions
Section 29 Section 31 Section 32 Section 33 Section 34 Section 35 Section 36
Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7
Exercise 8 Exercise 8 Exercise 8 Exercise 8 Exercise 8
Exercise 9 Exercise 9 Exercise 9 Exercise 9 Exercise 9
Exercise 10 Exercise 10 Exercise 10 Exercise 10
Exercise 11 Exercise 11 Exercise 11 Exercise 11
Exercise 12 Exercise 12 Exercise 12
Exercise 13 Exercise 13 Exercise 13
Exercise 14 Exercise 14 Exercise 14
Exercise 15 Exercise 15
Exercise 16 Exercise 16
Chapter 4 - Integrals
Section 38 Section 39 Section 42 Section 43
Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7
Exercise 8 Exercise 8
Exercise 9
Exercise 10
Exercise 11
Chapter 4 - Integrals (cont'd)
Section 45 Section 49 Section 52 Section 54
Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7 Exercise 7
Exercise 8 Exercise 8 Exercise 8
Exercise 9 Exercise 9 Exercise 9
Exercise 10
Chapter 5 - Series
Section 56 Section 59 Section 62 Section 66 Section 67
Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7
Exercise 8 Exercise 8 Exercise 8 Exercise 8 Exercise 8
Exercise 9 Exercise 9 Exercise 9 Exercise 9
Exercise 10 Exercise 10 Exercise 10
Exercise 11 Exercise 11 Exercise 11
Exercise 12 Exercise 12
Exercise 13
Chapter 6 - Residues and Poles
Section 71 Section 72 Section 74 Section 76
Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Chapter 7 - Applications of Residues
Section 79 Section 81 Section 84 Section 85 Section 87 Section 89
Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7
Exercise 8 Exercise 8 Exercise 8 Exercise 8 Exercise 8
Exercise 9 Exercise 9 Exercise 9 Exercise 9
Exercise 10 Exercise 10 Exercise 10 Exercise 10
Exercise 11 Exercise 11 Exercise 11
Exercise 12 Exercise 12
Exercise 13 Exercise 13
Exercise 14
Chapter 8 - Mapping by Elementary Functions
Section 90 Section 92 Section 94 Section 95 Section 96
Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7 Exercise 7 Exercise 7
Exercise 8 Exercise 8 Exercise 8
Exercise 9 Exercise 9
Exercise 10 Exercise 10
Exercise 11 Exercise 11
Exercise 12 Exercise 12
Exercise 13
Exercise 14
Chapter 8 - Mapping by Elementary Functions (cont'd)
Section 97 Section 98 Section 99 Section 100
Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6
Exercise 7 Exercise 7
Exercise 8 Exercise 8
Chapters 9 & 10 - Conformal Mapping and its Applications
Section 103 Section 106 Section 110 Section 112 Section 115
Exercise 1 Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5 Exercise 5 Exercise 5 Exercise 5
Exercise 6 Exercise 6 Exercise 6 Exercise 6 Exercise 6
Exercise 7 Exercise 7 Exercise 7 Exercise 7 Exercise 7
Exercise 8 Exercise 8 Exercise 8 Exercise 8 Exercise 8
Exercise 9 Exercise 9 Exercise 9 Exercise 9 Exercise 9
Exercise 10 Exercise 10 Exercise 10 Exercise 10 Exercise 10
Exercise 11 Exercise 11 Exercise 11
Exercise 12 Exercise 12
Exercise 13 Exercise 13
Exercise 14
Exercise 15
Exercise 16
Exercise 17
Exercise 18
Chapter 11 - The Schwarz-Christoffel Transformation
Section 117 Section 119 Section 122
Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4
Exercise 5 Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Chapter 12 - Integral Formulas of the Poisson Type
Section 124 Section 125 Section 127 Section 128
Exercise 1 Exercise 1 Exercise 1 Exercise 1
Exercise 2 Exercise 2 Exercise 2 Exercise 2
Exercise 3 Exercise 3 Exercise 3 Exercise 3
Exercise 4 Exercise 4 Exercise 4 Exercise 4
Exercise 5 Exercise 5
Exercise 6 Exercise 6
Exercise 7
Exercise 8