1. Prove the general formula for inversion in a circle C centered at ‰ with radius r. In particular, show in this case that p² ic(z) = - Zo + %0.

Q: 12. (a) 41 C NOT DRAWN TO SCALE In the diagram, O is the centrof the circle ABC and ZBCA= 41°. Find:…

A: We will solve both the parts of this question using only logic and some basic knowledge of geometry.

Q: 17. In the square above, each arc is from a circle of radius 1. What is the area of the shaded…

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Q: 17. Evaluate f. dr, where F(x, y) = centered at the origin. (²²²²), and C is the circle of radius 5

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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: Evaluate S, y2 – x ds for each of the following curves. a) C = c, is the line segment from (-5, -3)…

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Q: 2.x²y"+xy'–3y= 0,x>0

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Q: xx+24=5x² fpyonbouy of anyos

A: We have xx+24≤5x2 Consider:…

Q: 3. Compute : exp(i sin(e¯ni)).

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Q: Question 2. Construct with straight edge and compass (a) Given a point P and two circles w₁ and ₂…

A: Given that two circles w1 and w2 not passing through P. Condition for two circles to be orthogonal…

Q: 5. The graph of f(x, y) is shown to the right: Draw the following two cross sections and label the…

A: (a) slicing the surface parallel to x-z plane at y=0. (red line) So for f(x,0)

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

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Q: 3. MK and ML are tangent to circle J. If MK = 6x - 15 and ML = 2x + 9, find x.

A: Given,           MK and ML are tangent to circle J. MK=6x-15 and ML=2x+9.

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

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Q: Find f (x-y3)d a + xy dy if the contour C looks as follows: It consists of two arcs of radius 1 and…

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Q: follows N2. 6. Find the center and radius of the circle described by the equation r +y + 6x – 4y –…

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Q: Let f (2) = 5. Let C be the circle |z| = 2 in the counter-clockwise direction. What is 2ni Tf(2) dz?

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Q: Which of the following intograls will give the arca of the circle of radius 2? (Hint: (y h)^2-…

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Q: Question 10: Find the number of common tangents to circles x2 + y? + 2x + 8y – 23 = 0 and x? +

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Q: TC is a tangent to a circle at C and BA produced meets this tangent at T. Show that triangles TCA…

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Q: Consider the curve r(t) = (-2 sint, 2 cos t) on the interval t = [0,2π]. Compute . Explain what the…

A: We have to compute the curvature of the curve r→(t)=(−2sin⁡t,2cos⁡t), we first need to find the unit…

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

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Q: Show that the equation of a circle centered at zo with radius R can be written as |z|² - 2 Re(zzo) +…

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Q: Compute ž dz +y1 z dz, +72 and where +Y1 is the segment from 1 to -1, and +y2 is the arc on the unit…

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Q: Sp

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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: 10. AT is tangent to both circles K and J at A. ST is tangent to OK at S and RT is tangent to OJat…

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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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