2e? Let f (z) = -Let C'be the circle z = 7in the counter-clockwise direction. (z – 3) (z – 5) Part (a) Find | f(2) dzusing Cauchy's integral formula.

Q: Consider F and C below. F(x, y) = x² i + y² j C is the arc of the parabola y = 4x² from (-1, 4) to…

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Q: Q15) A complex-val functio is given in the following. f (2) = %3D a) Find real (u (x, y)) and…

A: Here we use definition of existence of limit to check  f(z) is continuous or not.

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: 2e Let f (2) Let C be the circle (z – 4) (z – 6) z = 8 in the counter-clockwise direction. - - Find…

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Q: Use Green's Theorem to compute y dx+(x³+3xy²) dy where C is the closed curve around the triangle…

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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…

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Q: (a) Let f(2) = (z +4-i) (z+ + 5z³) Using CRT, evaluate the integral f(z (2)dz, where the contour Cis…

A: According to our company policy, we are supposed to answer only one question at a time. For the rest…

Q: Ex(6):-(H.W) Find the center and the radius of the circle whose eq x'+ y' +x+3y 7

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Q: how that u(x, y) is harmonic in some domain and find a harmonic njugate v(x, y) hen: u(x, y) = 2x –…

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Q: Compute the line integral -xdy + ydx 2(x-y)2 +4xy where L is the circle (1-x)2 + y2 = 3 with a…

A: We can write the given line integral as ∫L y2x-y2+4xydx+-x2x-y2+4xydy, where L is the circle…

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

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Q: (a) Evaluate feay'ds with C being the right half of the circle + y - 16. Does it depend on…

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Q: (15) Given two functions u(x + y) and v(x + y), what is Vu × Vv? Don't show it using an example. If…

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Q: Let F = -yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by…

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

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Q: o F. ds, where F(x, y) = x²i+x²j and C consists of the arcs y = x² and y = x for 0 < x< 1.

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Q: P(Z) (2) Let P(Z) = a + bz + cz² and f dz = = $c P(Z) Z² dz = f P(Z) dz = 2πi Z3 where C is the…

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Q: F(x, y) = x² i + y² j C is the arc of the parabola y = 4x² from (-1, 4) to (0, 0) %3D (a) Find a…

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Q: Let f(z) = E (z – 5)" n4" (n + 2)2 n=1 i) ii) iii) Find the region where the function f(2) is…

A: The boarder of the image looks like square root of the term. But not it is square root. Please check…

Q: 1 Let f (z) = . Let C be the circle |2| = 2n the counter-clockwise direction. What is 2ri Lf(2) dz?…

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Q: z-72+3 Using Cauchy's Integral Formula Evaluate where c is the circle lIzl = 2. z+i

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Q: Consider f (x, y) 3x² + xy + 3y². Use calculus to find the extreme values of fon the circle x² + y²…

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Q: Which of the following statements is NOT correct? (A) The function u(x, y) = x² - y² is harmonic.…

A: Analytic and complex integral true false statements

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…

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Q: 2e² Let f(z) Let c be the (z-7)(z- 9) circle |z| = 11 in the counter-clockwise direction. Find…

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Q: Let F=-yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by…

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Q: The plane S can be parameterized by r(u, v) = (u, v, 3-u-2v with (u, v) E D, where D is bounded by u…

A: Introduction: The plane S can be parametrized by r→(u,v)=u,v,3-u-2v with u,v∈D, where D is bounded…

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

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Q: 2ez Let f(z) = Let c be the (z - 7)(z - 9)' circle |z| = 11 in the counter-clockwise %3D direction.…

A: Here , f(z) = 2ezz - 7z - 9 Let , C be the circle , z = 11. We know Cauchy - integral  formula,…