e (²+1)5 sin f(z) = sin ³ z 2³(2-3i)² # Compute the residue Res(f; zo), where zo is the pole.

Q: Find the constants a and b such that the complex function f(z) = x² + ay² - 2xy + bx²i − y²i + 2xyi,…

A: A function f(z)=u+iv is analytic if ∂u∂x =∂v∂y and ∂u∂y =-∂v∂xGiven…

Q: Verify that u(x, y) = x4−6x2y2+y4 is harmonic everywhere and determine its harmonic conjugate

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Q: u(x, y) = -e sinx - 2e* siny. Find a harmonic conjugate v of u, namely a function v such that the…

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Q: Let z = sin(7(z – 2y²)). None of these is true. (-1,1,–4(1– x). A normal to the tangent plane to the…

A: For a function z=fx,y, the tangent plane at point x0,y0 is defined as:…

Q: -3 if 0 6 The Fourier sine transform of f(x) is sin 3w a) 6 2 (sin 6w b) -3 1-cos 6w с) —3 -cos 3w…

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Q: 2) Find the Fourier transforms of: a) b) f(x) = cos(ax), where a > 0. f(x) = x² cos(ax) + x sin(ax),…

A: Since the given problem has multiple sub parts, as per our company guidelines we will solve only the…

Q: dw Let w = cos(6x – 6y), where × = r* and y = 3. Find A o dw = 18sin(6r* – 18)r³ dt O dy =…

A: Answer is Option b is correct Explanationo the solution is given below...

Q: Let r(t) = (sin(t), cos(t), 6 sin(t) + 9 cos(2t)). Find the projection of r(t) onto the xz-plane…

A: Given vector…

Q: 1] Evaluate (a) -S (s²+1) ² {t sin (b) S 1/2 5² (s² +¹)² (d) S

A: Find Laplace of tsin(t/2)

Q: Prove that B(m, n) = B(m + 1, n) + B(m,n + 1)

A: given,

Q: Evaluate the complex function. Find u(x,y) and v(x,y) f (2) = e=" O e3ry sin(3x²y + y*) O e-3ry…

A: To use the following problem we use the following result Z = x+iy  ez = e(x+iy) = ex( cosy +i siny)…

Q: Which of the following is a 1-form? In the case of a 1-form express it as a linear combination of…

A: A 1-form is a linear function ν: φpℝn→ℝ that is v∈φpℝn Given  φνp=ν·dx1,dx2,...,dxn…

Q: v=e2r-y cos (y– 2x) Obtain the value of of the relation дхду A 8e2r-y sin (y– 2x) B - 6e2 -y cos(y–…

A: Option (C) is the correct.To solve this question first we take the partial derivative with respect…

Q: az over the contour C |z = 4.5 sin z (b) Сompute

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Q: If v(1, y) is a harmonic conjugate of a harmonic function u(1,y) is also a harmonic function. show…

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Q: u(x, y) = -e sin x - 2e* siny. Find a harmonic conjugate v of u, namely a function v such that the…

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Q: Let C, be the rectangle with vertices (0,0). (1,0) (0,2) and (1,2) oriented counterclockwise. Find J…

A: Green's theorem problem....

Q: Can there exist two solutions y1, 42: [-10, 10] R to the ODE y = V1+ sin (ry) %3D with yi(-10)…

A: The given differential equation is  y'=1+sin2xy On simplifying this, y'2=1+sin2xy. Hence the…

Q: Find a so the function u(x, y) = e2" cos 2ay + a²x – y + 15 is harmonic. Then, find the complete…

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Q: 5. Find L{f(t)} a. f(t) = sin?(t) + t b. f(t) = n² – 8e¬2t + (et + 1)² | c. f(t) = F, sin yt -cos…

A: As per our limit we can solve only first three subdivisions if you want the answer for other…

Q: Evaluate sin sin(x) dx + z cos(y) dy + sin(y) dz where C is the elipse 25x² + 16y2 = 49, oriented…

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Q: Show that the function u = In(X² + Y2) is harmonic and find the conjugate harmonic v.

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Q: Show that u(x, y) = e³ cos x is harmonic and find the harmonic conjugate v such that v (0,0) = 0.

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Q: Let f(z) : D → C be a complex function. Is it possible for both f(z) and f(z) to be analytic? • If…

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Q: y3 be a harm C conjugate. D[ is equal to

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Q: 1. Evaluate f{(t² e2t + sinh2t)}

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: Let r(t) = (sin (1), cos (1), 4 sin (r) + 5 cos (2r)). Find the projection of r (t) onto the…

A: We have been given:rt=sint, cost, 4sint+5cos2t. To Do:We have to find the projection of rt onto the…

Q: 8. Consider the function -2r y = c₁e² cos 2x + c₂e² sin 2x + c3 + C₁x + c5е¯¯² + c6e- +c7xe-2x with…

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