8) Consider the function f(z) given by f(2)= 24-2 cos 20z² + 1. (a) Show that f(z) has zeros at eie, e-i, -eie and -e-ie.

Q: Suppose f(x) = sin 4-x). Evaluate: x) dx (A - 3cos FC B -cos 3 X-4+ C 3 Cos 3 (D) 3cos -x- 4)+C

A:

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

A:

Q: (b) Verify that the following function is harmonic u(x, y) = −e sin x - 2e-siny. Find a harmonic…

A: Here we have to verify that the function is harmonic and then find the harmonic conjugate.

Q: Let u = e-7*sin(7y). Then a harmonic conjugate of u is

A: If two given functions u(x,y) and v(x,y) are harmonic in a domain D and their first-order partial…

Q: F. dr Evaluate So

A: In this question, we have to evaluate the line integral for given vector function along the given…

Q: 3. If G = (2x²y – x*)î + (e*y + y sin x)j+ (x² cos y)k, find: %3D дхду

A:

Q: a) Use the definition of the hyperbolic functions to prove that 2cosh?(x)–1=cosh(2x). 1%3D

A:

Q: Verify that the given complex function is an Analytic Function, w = f(z) = 2z³ – 2z + 12

A:

Q: h(t) = / e -3(t-T) cos(27)dr. This is the convolution of two functions f(t) and Consider g(t). That…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: I of an analytic f hen the real part

A:

Q: Let u(x,y)=4x+3x2y−y3. Part (a) Show that u is a harmonic function. Part (b) Find a harmonic…

A: The given problem is to show that the given function u(x,y) is harmonic function and also to find…

Q: Given the complex function ƒ(z) = |z|² = x² + y². Where are f(z) differentiable? Where is it…

A:

Q: 25. Find the harmonic conjugate of u = In|z| and corresponding analytic function f (z) = u + iv.

A:

Q: əz Find ( (). If (x, y, z)variables, and (2) a function in (x, y), and achieve the equation: 1 x-2 +…

A:

Q: Q2: Show that u = ln(x² + y2) is harmonic function and find the conjugate harmonic v = (x. y) and…

A: Given: u(x, y)=lnx2+y2 To show: u(x, y) is harmonic function and find its harmonic conjugate v(x, y)…

Q: Given the complex function f(z) ee-iy. Where are ƒ(z) differentiable? Where is it holomorphic?…

A:

Q: If v(r, y) is a harmonic conjugate of a harmonic function u(x, y) show that the function g(r, y) =…

A: Harmonic function: A two variable function ux, y is said to be harmonic, if the function is twice…

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

A:

Q: Let u (z, y) = 8r + 3ay- y Part (a) Show that u is a harmonic function. Part (b) Find a harmonic…

A:

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

A:

Q: 4. Determine whether the pairs of functions are linearly independent or linearly dependent on the…

A:

Q: What is the range of f(r) = cos(x)? i) [–1, 1] ii) [0, 1] iii) (-∞, ∞) O i O i

A:

Q: Let f(z) : D C be a complex function. Is it possible for both f(2) and f(z) to be analytic? 2. • If…

A: Solution

Q: (0,3) C1:x² + y² = 9. (-3,0) C2 (3,0) Figure 1 Based on Figure 1 and given that F = y?i + (3xy +…

A: Greens theorem If D be the region enclosed by the curve C , Which is positively oriented, smooth,…

Q: |(0,3) C1:x2 + y? = 9. (-3,0) C2 (3,0) Figure 1 Based on Figure 1 and given that F = y²i + (3xy +…

A: We have to find the work done by the vector force F =y2i+(3xy+4x)j Where c is a smooth circle…

Q: Verify that the function u(x.y) x- 3xy -5y is harmonic in the entire complex plane ,And find the…

A:

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

A:

Q: 5- Verify that the given function u is harmonic in an appropriate domain D. Find v(x,y), the…

A:

Q: c) Let f(x, y,z) = cos (xyz)sin(x²y=

A: The given function is f(x,y,z)=cos2(xyz)sin(x2y2z2) ..............(1) we have to find;  fx=∂f∂x=?and…

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

A: