Question

Question 2. (a) [7 marks] Evaluate the integral ?_C dz / (1 + z^2) where C is the circle with centre -2i and radius 2 traversed anti-clockwise. (b) [8 marks] Let a be a fixed complex number different from zero. Let C_R denote the circle with centre at 0 and radius R ? |a| traversed anti-clockwise. What are the possible values of the integral ?_{C_R} (sin z) / (z - a)^3 dz? Justify your answer.

          Question 2.
(a) [7 marks] Evaluate the integral
?_C dz / (1 + z^2)
where C is the circle with centre -2i and radius 2 traversed anti-clockwise.
(b) [8 marks] Let a be a fixed complex number different from zero. Let C_R denote the circle with centre at 0 and radius R ? |a| traversed anti-clockwise. What are the possible values of the integral
?_{C_R} (sin z) / (z - a)^3 dz?
Justify your answer.

Question 2.
(a) [7 marks] Evaluate the integral
?C dz / (1 + z^2)
where C is the circle with centre -2i and radius 2 traversed anti-clockwise.
(b) [8 marks] Let a be a fixed complex number different from zero. Let CR denote the circle with centre at 0 and radius R ? |a| traversed anti-clockwise. What are the possible values of the integral
?CR (sin z) / (z - a)^3 dz?
Justify your answer.

Added by Jose Miguel J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/25/2023

Step 1

We have: $$\oint_C \frac{dz}{z^2 + 2}$$ where $C$ is the circle with center $-2i$ and radius $2$ traversed anti-clockwise. To evaluate this integral, we can use the residue theorem. Show more…

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Thanks for your feedback!

Question 2. (a) [7 marks] Evaluate the integral ∫_C dz / (1 + z^2) where C is the circle with centre -2i and radius 2 traversed anti-clockwise. (b) [8 marks] Let a be a fixed complex number different from zero. Let C_R denote the circle with centre at 0 and radius R ≠ |a| traversed anti-clockwise. What are the possible values of the integral ∫_{C_R} (sin z) / (z - a)^3 dz? Justify your answer.