(b) f2zdz where C is an arc of circle z = 2t3 + i(t – 4t3 + 2) - 1

Q: Let f (z) = 470 = Q A = 2and B= 2 + 2Let C1 be the contour composed of the line segments O Aand AB…

A: Let x(t) and y(t) be two real valued continuous function an[a, b] then z(t)=x(t)+iy(t), t∈[a,b] is…

Q: (ii) (iii) dz c (z²+4)³ where C is the circle |z-i=2 (z-1)dz (z+1)²(z-2)' 1- where C is the circle…

A:

Q: Pls help

A: We have to find the horizontal asymptote.

Q: Find the locus of the center of the circle touching the circle x\power{2} + y\power{2} − 4y - 2x = 4…

A: Let r and R be the radii of the required and the given circle,respectively.Let the center be…

Q: Use Green's Theorem to evaluate (V1+r) dr+2ry dy, where C is the triangle with vertices (0, 0),…

A:

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

A:

Q: Q2 Calculate 8- z dz, z(4-z)* where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: 5. Classify the given quadratic form. Make a change of variable x = Py, that transforms the given…

A: Given the quadratic from  Qx=x12+4x1x2-2x22 To make the quadratic form comparable to xTAx, we must…

Q: dz Find an upper bound for 9c z4 –5z²+6 dz, where c is the circle |z| = 4.

A:

Q: dz where C is cir

A:

Q: Let F (x, y) = 8Q A. Compute 82 yi+zj z² + y² and let C be the circle r(t) = (cost)i + (sin t) j. 0…

A:

Q: A line meets a curve y=2x-1 at the point (5,4). The line is tangent to the circde C:x +y² +10x+8y+…

A:

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: 323 + 4z2-5z+1 dz (z-2i)(23-2) 1. Compute: where C = {|z| = 3} is the circle of radius 3 centred at…

A:

Q: Prove that the curve y: (-,-)→ R³ is regular with factor H and determine whether the image y (t) =…

A: If γ't not equal to 0 for all t∈-π2,π2then it is regular. If γ''t=kγ't for all t∈-π2,π2 then the…

Q: Integrate h(x, y) = (x+y)i + (y²-x)j over the closed curve that begins at (-7,0), goes along the…

A:

Q: (b) Evaluate 2 + 5z zdz, 22 — 2х — 3 - where C' is a circle |z + 2| = 2.

A:

Q: O COsZ Sc (5 dz T. 4 2

A: Consider the equation, z-π2=1 This equation represents a circle plotted on the Argand Plane, with…

Q: Q3b): Compute zdz over several contours (i) The line from 1 to 1+ i. (ii) The circle of radius 1…

A: let fz=1z.  Since f(z) has an antiderivative in an open region D, then the line integral over given…

Q: Find the length of the curve y? = (x – 2)° between the points (2, 0) and (4, 2/2). 22/22 – 2/2 a)-…

A:

Q: Let F(x, y) == and let C be the circle r (t) = (cost)i + (sint)j, 0 ≤ t≤ 2π. A. Compute მი Note:…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the number of common tangents to the circles x\power{2}+y\power{2}+2x+8y-23=0 and…

A: For x2+y2+2x+8y-23=0 ,C1≡(-1,-4),r=210for x2+y2-4x-10y+9=0,C2≡(2,5),r=25now C1C2=distance between…

Q: Prove that the equation of any tangent to the circle x\power{2}+y\power{2}-2x+4y-4=0 is of the from…

A: