Show that, C : |z| = 3, |S, z3 – z?-3 c z4– z2+4 dz|s 117 TT 34 5. Evaluate 9. zt; sin 3z dz, where C is the circle |z| = 5

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: Determine a∈R such that ∫CF⋅dr = −2−(3π/4), where F (x, y) = (ay, (x^2 − y)/2) and C is the part…

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Q: B) Use Green's Theorem to evaluate /F-dr, where C is the circle r² + y? = 4 and F (r, y) = (y – 2…

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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: Let C be the arc of the circle [2] = R from z = R to z = -R Where R is a positive integer greater…

A: Given C be the arc of the circle z=R from z=R to z=-R, where R is a positive integers greater than…

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: Let C1 be the unit circle oriented counterclockwise, and let C2 be the circle of radius 2 centered…

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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: 2. Evaluateſ. a+ (z+30:) dz along C which is the circle |z + 3i| = 3, counterclockwise. %3D (z+3i)

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Q: If C is the unit circle x² + y² = 1 oriented counterclockwise and F(x, y) = x F. dR? -T 2π TT î 1 C…

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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: In the following sketch, O is the centre of the larger circle. PQ and PT are tangents to the smaller…

A: Given : O is center of larger circle and PQ and PT are tangents of a smaller circle. To prove :  PT…

Q: Set up and simplify (but do not evaluate) : 3x ds, where C is the arc of the circle r2 + y² = 4 from…

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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: .If C is the circle (traversed once counterclockwise) of radius 2 with center at z = 0, %3D 7e?…

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Q: an Prove that n! ell7. dz 2ni (Z)n+1 Where C is a circle 1Z| 3D1 %3!

A: We have to prove that ann!=12πi∫Ceazdzzn+1, where C is the circle z=1 Use theorem which is given…

Q: *17. In the figure, BD is a diameter of the circle. PQ is the tangent to the circle at A. If 2QAB =…

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Q: Evaluate the line integral 3xy® ds, where C is the right half of the circle x? + y? = 36.

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Q: In the given figure , the common tangents AB and CD to two circles with centres O and O' intersect…

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Q: Find the center C(h,k) and radius (a) :of the circle x² + y° – 4x – 4 C(4, 3/2), a = 5 O С (4, 0), а…

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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: Evaluate (25 + 2xy – 2y²) ds, where C is the part of the circle x² + y² = 25 in the first quadrant.…

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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: 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: The value of the integral ze -dz , where C is the circle z=2 traversed once in the 2z - 3 positive…

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Q: Please evaluate (3y – ein(e) dx + (7x + Vy* + 1) dy, where C is the circle a? + y = 9. Hint: use…

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Q: 4. If AB is a diameter of a circle with center P, and X ånd Y are polits UI circle such that XY…

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Q: A- Using Simpson s Rule to estimate the area of the circle (r-4), c (1, 0) with (n=4). B- Prove…

A: The equation of a circle having center C(1,0) and radius r=4 is given by: x-12+(y-0)2=42…

Q: 5.2 O is the midpoint of the circle below. 0 1 5.2.1 Why is Ô, = Ô2. %3D www 5.2.2 Prove ABO = DCO.…

A: Vertical angle: Vertical angles are angles opposite each other where two lines cross and they are…

Q: If C is the circle |2| = 2, given clockwise, then the integral Sc dz is (z–41)² Select one: O a. -2…

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Q: If R is the region in the first quadrant between the circles r = 1 and r = 2, and if f is continuous…

A: Given R is the region in the first quadrant between the circles of radii r=1 and r=2, centered at…

Q: Please evaluate P (3y – esin(@)) dx + (7x + Vyª + 1) dy, - where C is the circle x2 + y? = 9. Hint:…

A: See the details solution in below

Q: The DE for the family of circles of radius 9 is: A [1+ (y')²]³+81=0 B ® [1+(y")*]³–81=o [1+(y')²]³–…

A: The general equation of the circle with center (h,k) and radius r is             ( x - h )2 + ( y -…

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

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Q: Compute . Z+1 dz, where C1 is a part of a circle with r = 3, and 0<0< %3D

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Q: JK, KL, and LJ are all tangent to circle O (not drawn to scale), and JK E LJ .JA = 9, AL = 10, and…

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Q: In the following sketch, SET is a tangent to the circle. Prove that (1) 2 1 (2) 2. 3 2 41F

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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: 6. In the accompanying diagram, PQ is tangent to circle O at Q and PRT is a secant. If mZP - 56 and…

A: To find : m arc QR

Q: ež sin(z) Evaluate fr dz where I is the circle |z|=1 described in ccd.

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Q: In the diagram below, O is the centre of the circle. CDE is a tangent to the circle at D. DB bisects…

A: Solution as follow

Q: In the following sketch, O is the centre of the circle. AE= ED and DT=TC. %3D Prove that (1) Ê =Ô¡…

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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: z2 dz, where c is a unit circle. 3) Evaluate C 4z-i

A: Given : ∫Cz24z-idz Here, C is a unit circle. we can write it as 14∫Cz2z-i4dz it has singularity at…

Q: (i) Evaluate $.z'dz, where C is the positively oriented circle |z- 1| = 1.

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Q: RS is tangent to the circle at N. K 16. If m LK = 105, then m Z PNL = 17. If mPN m L PNR 100, then m…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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…

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

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