a-Compute the residue of the following functions in two different ways and what is the type of singular points: 1- at the singular point z = zo where zo + z1 and zo # z2 1 f(z) = (z – zo)(z – 21)(z – z2) 2- at z = 0 sin z f(z) = z4 %3D

Q: S[y] given by y = cosh æ + B sinhx, 0 0,

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Q: 24(z + i) (z - 4)5 (22 + 4)(z – 5) f(2), -dz integral value calculate. Y. F(2) c : |2| = 3 ve f(2) =…

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Q: Let z = e**y* , x = tan¬²(st5) and y = əz Evaluate as (2s+t)²* Select one: O a. 2xy³e{x³y?} t5 t –…

A: Given,

Q: 10.2 Evaluate f(0,1) f(2) dz when f(z) is (i), (ii) (Rez)², (iii) z-2 (4-1), (iv) sin z. (Use the…

A: To find : ∫γ(0;1)fzdz when  (i) z4 (ii) Re z2 (iii) z-2z4-1 (iv) sinz

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A: Use the definition

Q: The finite difference approximation of the first derivative in the explicit method used to solve…

A: For the first derivative .

Q: 3. Show that the function f(2)=√Im(2²) satisfies the Cauchy-Riemann equations at z = 0, but is not…

A: Given: fz=Imz2. To Do: Show that the given function satisfies the Cauchy-Riemann equations at z=0,…

Q: 1. Let f: R² → R2 be the function defined by f(x, y) = (x + 2xy, y² — x² − y). (a) Show that the…

A: If z=x+iy then equivalently we can write z=(x,y) if f(z) is a complex valued function &…

Q: Find the residues of the followings functions at z = 0: (1) (z² + 1)/z (2) (z² + 3z – 5)/2³ (3)…

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Q: 1 1 LGt-5- At²est + Ceisinh Dt = [(s – 1)3 ' s² + 2s – 5]

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Q: u = t+1.3 -sin(u+t +5.09) with u(1) = 0.29 Let . Approximate the maximum value of ult) to 5…

A: If any function has a maximum value at a point , then at that point derivative of the function is…

Q: 2 4) + +2 +2

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Q: Q4. (a) Give A = 2xy â, +3â, +z'yâ,, calculate v.AdV as shown in Figure Q4(a). A, (0, 1, 1) (0,0, 1)…

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Q: Satisfies the Cauchy-Riemann equations at point z=0. Is the function analytic at z=o? Justify your…

A: By the sufficient condition of the analytic function or differentiability of the complex function,…

Q: Let (z-a)" dz where a € C and the parameterization of the curve is a = {|z| = r}. Apply the…

A: Hint: The statement of fundamental theorem  of complex analysis is: If a continuous function f has…

Q: Now, 2 x (+) dt 2 50, d2x(+) dt 2 -1 d2x(1) dt 2 is +2 J2x(+) ct 2 + 1 +2 = -15(++ 2) + 25 (1-0) +…

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Q: f(x,y) = –x² + 2xy + 3y² – 6x – 2y – 4 | - Serialize the function around the point (-2,1). a) f(x,y)…

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Q: D(D² + 9)y = sin3x - 5

A: Using method of linear differential equation with constant coefficient.

Q: Let ƒ(z) = f(x + y) = (x² - y² − 2x) +i (2y - 2xy) be a complex function. Where is the function…

A: According to the question,

Q: 2-Prove that: B (m, n)-ß (a,m) 3- Simplify to the simplest: (2+0(1-0) (1+0)(3-2)

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Q: Which of the following functions do not form a set of fundamental solutions of y" - 4y 0 Select one:…

A: We will find out the required set which don't form a fundamental set of solution.

Q: Let Ci and co be arbitrany canstants. Geneial solutian to the hamogencus dfferenti al oquation 1692…

A: Given differential is Cauchy Euler's differential equation

Q: Show the following functions are holomorphic on the domains given, and compute their derivative…

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Q: 3 is the imagina u =

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Q: 2 4. Find the most general analytic function f(z) of the variable z = x+iy whose imaginary part is…

A: 4. Given vx, y=y-yx2+y2 as the imaginary part of the complex function f(z).   To Find: The most…

Q: 50, dex(+) = -25 (+ + 2) + 25 (1-0) + 15 (t-1) at 2 = -√(x + 2) + 251f) + 5lt-2) By using…

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Q: Suppose f1 and f2 are two analytic functions so that Re(f1)=u and Re(f2)=u.  Then h(z)=f1(z)-f2(z)…

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