Question

Q3: Apply the Cauchy-Goursat theorem to show that ?_c f(z)dz = 0, when the contour C is the unit circle |z| = 1 in either directions (a) f(z) = z² / (z-3) (b) f(z) = 1 / (z²+2z+2) Q4: let C denote the positively oriented boundary of the square whose sides lie along the lines x = ±2 and y = ±2, evaluate ?_c e^-z / (z - (?i/2))

          Q3: Apply the Cauchy-Goursat theorem to show that ?_c f(z)dz = 0, when the contour C is the unit circle |z| = 1 in either directions
(a) f(z) = z² / (z-3)
(b) f(z) = 1 / (z²+2z+2)

Q4: let C denote the positively oriented boundary of the square whose sides lie along the lines x = ±2 and y = ±2, evaluate ?_c e^-z / (z - (?i/2))

Q3: Apply the Cauchy-Goursat theorem to show that ?c f(z)dz = 0, when the contour C is the unit circle |z| = 1 in either directions
(a) f(z) = z² / (z-3)
(b) f(z) = 1 / (z²+2z+2)

Q4: let C denote the positively oriented boundary of the square whose sides lie along the lines x = ±2 and y = ±2, evaluate ?c e^-z / (z - (?i/2))

Added by Rosa M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

06/14/2023

Step 1

(a) f(z) = 2z - 3 (b) f(z) = 2z^2 + 2z + 2 The contour C is the unit circle |z| = 1. Now, we will apply the Cauchy-Goursat theorem. The theorem states that if a function is analytic (holomorphic) inside and on a simple closed contour C, then the integral of the Show more…

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Q3: Apply the Cauchy-Goursat theorem to show that ∫_c f(z)dz = 0, when the contour C is the unit circle |z| = 1 in either directions (a) f(z) = z² / (z-3) (b) f(z) = 1 / (z²+2z+2) Q4: let C denote the positively oriented boundary of the square whose sides lie along the lines x = ±2 and y = ±2, evaluate ∫_c e^-z / (z - (πi/2))