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Evaluate o zdz, where C is the circle |2| = 4 taken with counter-clockwise (i.e. anti- clockwise) orientation. Hint: Let C: z(t) = 4 cost + i4 sint for 0 ≤t≤2. (Ans: 0) Evaluate fozdz, where C is the circle |2| = 4 taken with counter-clockwise (i.e. anti- clockwise) orientation. (Ans: 32πi) Evaluate fo(z+1)dz, where C is given by z(t) = cost + i sint for 0 ≤ t≤ π/2. (Ans: i-2) - Evaluate o zdz, where C is the line segment from i to 1 and z(t) = t + (1 − t)i for 0≤t≤1. Evaluate for z²dz, where C is the line segment from 1 to 1+i and z(t) 0 ≤t≤1. (Ans: 1) = 1 + it for (Ans: 1+2i/3)

Evaluate o zdz, where C is the circle |2| = 4 taken with counter-clockwise (i.e. anti- clockwise) orientation. Hint: Let C: z(t) = 4 cost + i4 sint for 0 ≤t≤2. (Ans: 0) Evaluate fozdz, where C is the circle |2| = 4 taken with counter-clockwise (i.e. anti- clockwise) orientation. (Ans: 32πi) Evaluate fo(z+1)dz, where C is given by z(t) = cost + i sint for 0 ≤ t≤ π/2. (Ans: i-2) - Evaluate o zdz, where C is the line segment from i to 1 and z(t) = t + (1 − t)i for 0≤t≤1. Evaluate for z²dz, where C is the line segment from 1 to 1+i and z(t) 0 ≤t≤1. (Ans: 1) = 1 + it for (Ans: 1+2i/3)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Evaluate o zdz, where C is the circle |2| = 4 taken with counter-clockwise (i.e. anti- clockwise) orientation. Hint: Let C: z(t) = 4 cost + i4 sint for 0 ≤t≤2. (Ans: 0) Evaluate fozdz, where C is the circle |2| = 4 taken with counter-clockwise (i.e. anti- clockwise) orientation. (Ans: 32πi) Evaluate fo(z+1)dz, where C is given by z(t) = cost + i sint for 0 ≤ t≤ π/2. (Ans: i-2) - Evaluate o zdz, where C is the line segment from i to 1 and z(t) = t + (1 − t)i for 0≤t≤1. Evaluate for z²dz, where C is the line segment from 1 to 1+i and z(t) 0 ≤t≤1. (Ans: 1) = 1 + it for (Ans: 1+2i/3)
Transcribed Image Text:Evaluate o zdz, where C is the circle |2| = 4 taken with counter-clockwise (i.e. anti- clockwise) orientation. Hint: Let C: z(t) = 4 cost + i4 sint for 0 ≤t≤2. (Ans: 0) Evaluate fozdz, where C is the circle |2| = 4 taken with counter-clockwise (i.e. anti- clockwise) orientation. (Ans: 32πi) Evaluate fo(z+1)dz, where C is given by z(t) = cost + i sint for 0 ≤ t≤ π/2. (Ans: i-2) - Evaluate o zdz, where C is the line segment from i to 1 and z(t) = t + (1 − t)i for 0≤t≤1. Evaluate for z²dz, where C is the line segment from 1 to 1+i and z(t) 0 ≤t≤1. (Ans: 1) = 1 + it for (Ans: 1+2i/3)
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