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)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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