5. If z is any point on the circle |z1 – 2| = 2, then prove that - 2 arg(z – 2) = 2 arg z = arg (z² – 2z). | 3 z²-z 3 6. On |z| = 2, show that Iz4-3z+2| |z3+z²_3| 39 1. On |z| = 3, show that z3+8 19

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Q: Which one of the following equations describes the circle in the xyxy-plane with centre…

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Q: 6. Given a rule x² + y² = 9, its image rule x? + y² – 2x + 6y +1 = 0 under a translation, state a…

A: To solve the given translation problem.

Q: 6. State the center and radius of the circle: x + y² – 4x + 2y = 16 Center: (-2, 1) and r = 21…

A: The solution as follows :-

Q: 2. Find the area of the ring formed by the circles whose equations are (x + 4)2 + (y- 3)2 = 25 and…

A: Since you have posted multiple questions i can do first question (2,3,4) as per our company…

Q: If z = x + iy, then the inequality |z – i| < 2 is a: A. Circle with center at (0,1) and radius 2. B.…

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Q: Use Green's Theorem to find SF ·dř where F = (y³, –x³) and C is the circle x² + y² = 3. %3D %3D

A: The given vector is  F = y3i - x3j

Q: X. Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1,-1) to (0,0), C₂ is the line segment…

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Q: 6. Given a rule x2 + y2 = 9, its image rule x2 + y2 – 2x + 6y + 1 = 0 under a translation, state a…

A:

Q: Exercise 1.2.16 Find the circle x²+y² +ax+by+c=0 passing through the following points. а. (-2, 1),…

A: a) The given equation of the circle x2+y2+ax+by+c=0 Since the points (-2, 1), (5, 0) and (4, 1)…

Q: (3) Consider the quadric surface SC R, having equation a2 + y? – 22 = 9. Find all lines through P =…

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Q: 2.2 Find upper bound of z + 4 -dz (z – 3i)3 + 1 where C is the circle |z – 3i| = 4.

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Q: Suppose that C = {z:|2| = 1} is the unit circle, followed in the positive (anticlockwise) direction.…

A: Given: C=z:z=1is the unit circle  f(z)=∫cdz4+3z

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: Use Green's theorem to find $ x? ydr + xdy over a counterclockwise triangular path passing though…

A: To find the line integral ∮x2ydx+xdy by using Green's theorem, First, we need to draw the given…

Q: 3. a) Compute: f (Rez-3z) dz where I is a directed line segment from z = 0 to z = i. b) Let C be the…

A: To Evaluate:  (a) ∫Γ(Rez-3z)dz , where Γ: z=0 to i. (b) ∮Ce-zz2(z-5)dz, where C: |z|=4 oriented…

Q: Formulate an verify Green theorem when [P, Q] = [2yx, y² + 2x] and the curve y is the positively…

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Q: If a bug walks on the sphere x^2 + y^2 + z^2 − 4x + 4y + 4z + 3 = 0 how close and how far can it get…

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Q: 1- What is the value of f 3z2+7z+1 dz z+1 (a) If C is the circle |z+1|=1. (b)If C is the circle…

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Q: Prove that the circles x² + y2 + z2 - 2x + 3y + 4z - 5 = 0, 5y + 6z +1 = 0 x² + y2 + z2 - 3x - 4y +…

A: We will use equation of sphere passing through sphere S  and plane P  S+λP =0

Q: Find a parametric description for the circle x2+y2-6y=0, oriented clockwise and where t begins at 0.…

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Q: Here are the graphs of the circle centered at (0,0) with radius 8 and the line given by 4x +7y = 65.…

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Q: Q5. Prove that the circle {(x, y), x² + y² = 1} is not homeomorphic to the interval [-1, 1].

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: Calculate both sides of Green's Theorem when F = [-x²y, xy²] and y positively oriented circle x2 +…

A: According to the given information it is required to calculate both sides of the Green’s theorem.…

Q: 3. a) Compute: f (Rez-32) dz where I is a directed line segment from z=0 to z=i. b) Let C be the…

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Q: 2.2 Find upper bound of z +4 -dz - 3i)3 +1 where C is the circle |z – 3i| = 4.

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Q: Suppose a point X lies in the exterior of a disk, and suppose that two lines are drawn from X…

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Q: Evaluate f 3z2dz over C, where C is the upper half circle |z – connects points O and 1+i. -글히 %3D플…

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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: If z = x + iy, then the inequality |z + il < 3 is a: A. Circle with center at (0,1) and radius 3. B.…

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Q: Which of the following is a point on the sphere with radius r = 3 centered at the point (-1,0, -1)?…

A: We have given a center and radius of sphare

Q: + 4z 53. Use (7.8) to evaluate dz around the circle |z – 2i| = 2. - z4 + 8z2 + 16

A: Given,  ∮z3+4zz4+8z2+16 dz  around the circle z-2i=2

Q: 4. Let C be the the circle ² + y² = 4 and Calculate the work(W = [,F dr when C is traversed in the…

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Q: 4. Evaluate / (z – 2) dz where C is the lower half of the circle |2 – 2| = 4.

A: Note: According to bartleby guidelines we have to answer only first question please upload the…

Q: Exercise 1.2.16 Find the circle x2 +y² +ax+by+c=0 passing through the following points.

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Q: 2z-1 Find the upper bound of where C is the right half of the z* +5z +4 circle |z|= R, R>2

A: Given, I=∮c2z2-1z4+5z2+4dz, z=R, R&gt;2 Now, fz=2z2-1z4+5z2+4 For singularities of fz, we have,…

Q: Let C be a circle with |z - i| = 3 travelled once in counterclockwise direction. Evaluate: 5z3 + 3z2…

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Q: A Bezier curve is defined by PO (0,0), PI (2,5), P2 (5,5) and P3 (7,0). Sub divide the curve at u…

A: We will get only one point as we have only one value of u. The given points are P00,0, P12,5, P25,5,…

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: Let C consist of the part of the circle r +y = 4 from (2,0) to (0,2), Followed by the line segments…

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Q: Q5. Prove that the circle {(x, y), z² + y² = 1} is not homeomorphic to the interval (–1, 1). 1

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Q: Part (a) Evaluate 100e dz, where C is the polygonal path consisting of the line segments from z =…

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Q: Find the value of o(4x + y)dy - rydy where C is the path around the triangle in the counterclockwise…

A: According to our guidelines we can only answer one question at time, rest you can repost. The given…

Q: 4. For a family of circles with center at (5, 6), determine its corresponding DE. A. (x – 5) + (y-…

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Q: Let G₁ be z = 6-√√36 - x² - y² and G2 be the upper nape of x² + y² - 3z² = 0. If S is the circle…

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

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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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