8. If C'is the circle |z – 1| = In the counter-clockwise direction, what is fa sScdz? z-1 27i 2rie 2rie-1

Q: 3. a) Compute : S, (Re z – 3z) dz where r is a directed line segment from z = 0 to z = i . b) Let C…

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Q: 1 dz (z² + 9) Let Cb the circle |z - 3i| = 2. Then (6+ 32 2 πί TT 3 O none of these

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Q: 4. Compute, ydx + xdy x² + y² where C is the circle centered at the origin of radius 2 oriented…

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Q: 1 Evaluate 2 4 |dz , (z+ 5i) 3 niPc54 + Z+ 5i where C is the circle |z + 5i| = 4 + 2, 0 s 0 < 2n .…

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Q: 13.10. Let y be the circle |z| = 2. Show that 1 dz- z2 – 1 3

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Q: Evaluate 8 1 Ti fc 101 dz , (z+10i)³ ] z+10i where C is the circle |z+ 10i| = 1 + 8, 0 < 0 < 27 .

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Q: By Green's theorem, if C is the circle x2 + y? = 4 taken anticlockwise, then fv dz - z'dy, equals…

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Q: 4. Let C be the circle |z| = 2 traversed once in the positive sense cos 3z (counter clockwise).…

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Q: 4. Let C be the circle |z| = 3 traversed once in the positive sense 2z-17 (counter clockwise).…

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Q: e? – 1 (b) ( - 1y2 dz where C is the positively oriented circle |2| = 3. %3D z(z – 1)2

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Q: Let F(x, y) = 4yi + (2æ + ev* ); Calculate ,F · dr, where C is the circle of radius 2 centered at…

A: Given that F(x,y)=4yi+2x+ey2j The objective is to calculate ∫CF.dr where C is the circle of radius 2…

Q: Find the areas of the regions Shared by the circle r = 2 and the cardioid r = 2(1 - cos θ)

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Q: B) Evaluate S Ln z dz around the circle | z| = 2 %3D

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Q: If C'is the circle of radius 3 centered at the origin, starting at the point (3,0) and moving around…

A: Answer and explanation is given below..

Q: 3. Let C be the circle Iz| = 3, described in the positive sense. Show that if 2s2-s-2 ds (Izl # 3),…

A: Given: g(z)=∫C2s2-s-2s-zds

Q: 4. Let C denote the circle |z – 2i| = 1, taken in the usual counterclockwise orientation. Compute by…

A: Given: Let C  denote the circle z-2i=1 z-2i=1x+iy-2i=1x+iy-2=1 So, Centre of circle will be 0,2 and…

Q: 6. Evaluate [(x + y²)dx – xdy where C is the circle "x²+y² : = 1" with a counter- clockwise…

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Q: 글 36- +| de. 1 4 dz, (z+3i)³ ] Evaluate - z+3i where C is the circle |z+ 3i| = 6 + 4, 0 < 0 < 2ñ .

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Q: 4. Let C be the circle |z| = 2 traversed once in the positive sense (counter clockwise). Compute :…

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Q: 4. Let C be the circle [z| = 4 traversed once in the positive sense %3D sin 3z (counter clockwise).…

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Q: 2: Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x–2)²+(y-3)² = 4 | a) Using Green's Theorem

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Q: 6. Let C C R? be the positively-oriented boundary of the graph of the circle x2 + y? = 1. Using…

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Q: =2) Calculate & ydx + xz² dy - zy³ dz, where c is the circle x² + y² = 4, Z=3 (conterclockwise)…

A: We will use stokes theorem to find integral

Q: Re(z) dz, where C is the right half circle |2| = 3, from z 2² – 2i (Ъ) -3i to z = 3i.

A: To Determine :-  An upper bound of the absolute value of the integral. ∫C Re zz2 - 2i dz  where C is…

Q: where C is the circle |z = 3i| =4. 2.3 Use the Cauchy integral formulae to evaluate 22 1 (9 – 22)(2…

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Q: Integrate counterclockwise around the circle |z – 6i| = 3. z(z – li)? - NOTE: Enter the exact…

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Q: Please evaluate (3y – einl2) dr + (7x + V yt + 1) dy, where C is the circle x² + y² = 9. Hint: use…

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Q: 2.2 Prove that ne ? ++1 p- 3 where C is the arc of the circle |2| = 3 from z = 3i to z = -3. %3D

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Q: 4. Evaluate y ds where C is the upper half of circle x² + y² = 9, traversed in the counterclockwise…

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Q: Verify Green's theorem for $[xy² dx + x²y dy], where y is the circle x? + y² = 4.

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Q: 4. Let C be the circle |z| = 2 traversed once in the positive sense cos 3z (counter clockwise).…

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Q: 3. Let C be the positively oriented circle |2| = 2. Compute the following integral: 726+글 exp(를)…

A: We have to find complex integral using Cauchy Gaurast Theorem. Cauchy-Goursat Theorem. If a function…

Q: Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x-2)²+(y-3)² = 4 Without using Green's Theorem.

A: We will find out the required value.

Q: 4. Let C be the circle |z| = 2 traversed once in the positive sense (counter clockwise). Compute: .…

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Q: 17. Evaluate OF . • dr where C is the circle x +y² = 1, z = 0 and F=yi+zj +xk.

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Q: 23 +3 Evaluate the integral dz, where C is the circle (a) |z + 3| = 3, (b) |z| = 3, (c) |z| = 7. 22…

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Q: Evaluate P (3x + 4y) dx + (2x – 3y) dy where 'C is the circle x?+y = 4.

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Q: i fc 78 8 Evaluate dz, where C is the circle |z+ 7i| = 8+6, 0<0< 27 z+7i (z+78)"

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Q: 2.2 Prove that ne dz < 3 e 2 ++1 whore C is the arc of the circle 2| = 3 from z = 3i to z = -3. %3D

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Q: Use Green's Theorem to evaluate - – In(x² + y²))dx + 2 tan¬²(y/x) dy, C is the circle (x - 4)² + (y…

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Q: 6. Compute G.T ds if K is the portion of the circle x2 + y* = 7 in the third quadrant (oriented…

A: region of integration is part of circle, x2+y2=7, lying in 3rd quadrant, thus, limits of x,y are -7…

Q: 5. Evaluate (y +tan x)dx+(x -2ry+y)dy, where C is the circler +y' =4 and is oriented in a positive…

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Q: 2. Use Green's theorem to evaluate fe e-x³ dx + (5x + sin(y²)) dy, where C is the circle x² + y² = 4…

A: Please see the below picture for detailed solution.

Q: Find the upper bound of |[∫c ez^2 + 1 / (z - 1)2 + 5] dz|, where C is the circle |z - 1| = 2.

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Q: 4. Let C be the circle |z| = 4 traversed once in the positive sense sin 3z (counter clockwise).…

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Q: 10. (~Ch16 Review #17) Use Green's Theorem to evaluate | x?y dx – xy? dy where Cis ,2 the circle x2…

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Q: Show that = sin t if t>0 and C is the circle z] = 3. 2mi Jz+1

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let CR denote the upper half of the circle |2| = R for some R> 1. Show that eiz 1 22 + z+1 (R – 1)2…

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Q: Let C be the circle |z| = 4 traversed once in the positive sense (counter %3D clockwise). Compute :…

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Q: 4. Let C be the circle |z| = 2 traversed once in the positive sense (counter clockwise). Compute : .…

A: Cauchy integral formulae: Let f(z) be analytic in a region D, derivatives of all orders are also…