(a) Jo (b) Jo 2 1 z² - 5z +6 e³z 1 5z + 6 (b) √ 1 €/ Use Cauchy's Residue Theorem to evaluate the integrals dz, where C is the positively oriented circle |z| = 4. dz, where C is the positively oriented circle |z| = 5/2. dz, where C is the positively oriented circle |z| = 2. +2²

Q: (a) Let f(z) = (z +4-i(z4 +5z®) Using CRT, evaluate the integral Of(2)dz, where the contour C Cis…

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Q: (b) Using the Residue Theorem, or otherwise, compute z-7 -z-2 dz, where C is the positively oriented…

A: Useful result:

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Q: where C is the circle with positive orientation. e2021z dz Yo (22 + 4)² (2² – 1) (a) C: |2 – 2 – i|…

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Q: Sc₂²2²4 dz, z-7 z²+z-2 where C is the positively oriented circle of radius 4 centered at z = 0.…

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Q: If the circle x² + y² + 2gx+2fy + c = 0 bisects the circumference of the circ x² + y² + 2g′x + 2ƒ'y…

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Q: (b) Using the Residue Theorem, or otherwise, compute Sezz z-7 -22²-22-2 dz, where C is the…

A: We shall first split the integral into partial fractions and then use Cauchys integral formula

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A: In polar coordinates,                                   and

Q: Calculate the following integral 1 Lc (z − 1) (2³ — 1) dz for each of the following contours C. In…

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Q: Using the Residue Theorem, or otherwise, compute z-7 z²+z-2 dz, where C is the positively oriented…

A: Let  fz = z-7z2+z-2           Consider  z2 + z - 2 = 0…

Q: -10y 10x Compute ſ. F · dr, where F(x, y) = and C is a circle of radius 20 with center at the origin…

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Q: b

A: Part (a): exp(-z) / (z^2 - 1)Identify the singularities: The function has simple poles at z = 1 and…

Q: (b) Using the Residue Theorem, or otherwise, compute z-7 z²+z=2 dz, where C is the positively…

A: Let  fz = z-7z2+z-2           Consider  z2 + z - 2 = 0…

Q: (a) Let R > 5 and let CR be the closed, anticlockwise contour obtained by joining the line segment…

A: Using residue Theorem:

Q: M2. Let C be the positively oriented circle |z1|-2 in the complex plane. Which of the following is…

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Q: 23 + 3 4. Evaluate the integral dz, where C is the circle (a) |z + 3| = 3, (b) |z| = 3, (c) |z| = 7.…

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Q: Let S = O (D), where D = {(u, v): ² + ² ≤ 9,u ≥ 0, v≥ 0} and ℗ (u, v) = (2u + 1, u − v, 3u + (a)…

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Q: Use Cauchy's Integral Theorem to evaluate fr 12z-3(2-42 dz where I' is the circle |z| = 2 described…

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Q: dz 5. Evaluate the integral where C is the circle (a) |z| = 1, (b) |z+3| = 2, (c) |z – 3| = 2. 23(z…

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Q: - Let f(x, y) = x² + y²-4 and let C be the circle x² + y² = 9 traced once counterclockwise. Evaluate…

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Q: We will try to compute the real integrale-1²/²e-itz dr. Let R> 0 and let y be the rectangle with…

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Q: Determine the integral f(z) dz around the clockwisely oriented triangle with the vertices ₁ = -1, 22…

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Q: Using the Residue Theorem, or otherwise, compute 2-7 +z-2 dz, where C is the positively oriented…

A: Let  fz = z-7z2+z-2                consider  z2+z-2 = 0…

Q: Show that 7(u, v)= (²-²,2ue) maps the triangle-((u, v):05≤SS 3) to the domain D bounded by z = 0, y…

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Q: Also apply Residue theorem to find the coSTz? value of the integral . C:|z + 1| = 3 (z+1)2(z-2)

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Q: EVALUATE § 7. d² USING STOKE'S THEOREM 3xz^ + ex² ₁ + 2xy^ с F(x, y, z) = 3XZ1 te C IS THE CIRCLE…

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