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Let f(z) = 5z + 14, and let C1 be the line segment from z = 0 to z = 2, let C2 be the line segment from z = 2 to z z = 0. Let C be the union of the curves Cı, C2, C3, i.e., C is the triangle formed from C1, C2, C3. Compute the integral ſc f(z)dz. 2+2i, and let C3 be the line segment from z = 2+ 2i to

Let f(z) = 5z + 14, and let C1 be the line segment from z = 0 to z = 2, let C2 be the line segment from z = 2 to z z = 0. Let C be the union of the curves Cı, C2, C3, i.e., C is the triangle formed from C1, C2, C3. Compute the integral ſc f(z)dz. 2+2i, and let C3 be the line segment from z = 2+ 2i to

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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Let f(2) = 11z + 11, and let C1 be the line segment from z = 0 to z = 2, let C2 be the line segment from z = 2 to z = 2+ 2i, and let C3 be the line segment from z = 2+ 2i to z = 0. Let C be the union of the curves C1,C2,C3, i.e., C is the triangle formed from C1, C2, C3. Compute the integral ſc f(z)dz. Solution: We see that fdz fdz + fdz + fdz. We first compute fa. f(z)dz. We see that along the line segment C1, y = 0, and thus z = x + iy = x, where 0 < x < 2. Hence dz = dx + idy = dx. |f(e)dz = (11z + 11)dz (11x +11)dx = (11x + 11)dx = (11/2)a²|;+11xß = 22 + 22 = 44. We now compute fa. f(z)dz. We see that along the line segment C2, x = 2, and thus z = x + iy = 2+ iy, where 0 < y< 2. Hence dz = dx + idy = idy. (11z + 11)dz = L (11(2 – iy) + 11)idy C2 = i (33 – 11iy)dy = 33iy3 + (11/2)g 6 = 66i + 22 Finally, we now compute Sa f(z)dz. We see that along the line segment C3, y = x, and thus z = x+ix = (1+i)x, where 0 <x < 2. Note that because of the direction of
Transcribed Image Text:Let f(2) = 11z + 11, and let C1 be the line segment from z = 0 to z = 2, let C2 be the line segment from z = 2 to z = 2+ 2i, and let C3 be the line segment from z = 2+ 2i to z = 0. Let C be the union of the curves C1,C2,C3, i.e., C is the triangle formed from C1, C2, C3. Compute the integral ſc f(z)dz. Solution: We see that fdz fdz + fdz + fdz. We first compute fa. f(z)dz. We see that along the line segment C1, y = 0, and thus z = x + iy = x, where 0 < x < 2. Hence dz = dx + idy = dx. |f(e)dz = (11z + 11)dz (11x +11)dx = (11x + 11)dx = (11/2)a²|;+11xß = 22 + 22 = 44. We now compute fa. f(z)dz. We see that along the line segment C2, x = 2, and thus z = x + iy = 2+ iy, where 0 < y< 2. Hence dz = dx + idy = idy. (11z + 11)dz = L (11(2 – iy) + 11)idy C2 = i (33 – 11iy)dy = 33iy3 + (11/2)g 6 = 66i + 22 Finally, we now compute Sa f(z)dz. We see that along the line segment C3, y = x, and thus z = x+ix = (1+i)x, where 0 <x < 2. Note that because of the direction of
Let f(z) = 5z + 14, and let C1 be the line segment from z = 0 to z = line segment from z = 2 to z = 2+2i, and let C3 be the line segment from z = z = 0. Let C be the union of the curves C, C2, C3, i.e., C is the triangle formed from C1, C2, C3. Compute the integral Se f(z)dz. 2, let C2 be the :2+2i to
Transcribed Image Text:Let f(z) = 5z + 14, and let C1 be the line segment from z = 0 to z = line segment from z = 2 to z = 2+2i, and let C3 be the line segment from z = z = 0. Let C be the union of the curves C, C2, C3, i.e., C is the triangle formed from C1, C2, C3. Compute the integral Se f(z)dz. 2, let C2 be the :2+2i to
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