и (х, у) 3D х3 +х — 3ху? What is the imaginary part of the analytic complex function if(z) = u(x, y) + i v(x, y) whose real part is given above?

Q: Use He Residue Heorem cnd evaluate the complex integra de cver the contour C:lal= 3/2 2(2+1)(2+2)

A: ∮Cz2+1zz+1z+2dz    C:z=32 To find : evaluate integral using residue theorem.

Q: 1. Use Cauchy- Reimann Equations to identify if it is differentiable or not, if yes then…

A: In the given question we have to check the differentiability of the given complex functions./…

Q: Let f(2) = Re(z) be a complex valued function defined on a complex plane С. Where is f…

A:

Q: The real and imaginary parts of z=x+iy are Rez=y €R Imz=y €R Rez=x ER Imz=x ER

A: Given complex number is z=x+iy.

Q: Qss- Prove that fcz) = cx=y') + ( are harmonic function of C, y) ,but are not . hormonic conjugates.

A:

Q: Find the number of zeros of f(z) = z' + iz² – z + 2i in the upper half-plane.

A:

Q: Let f(Z) = y – 2xy + i(-x + x² – y²) + z² where Z = x + iy is a complex variable defined in the…

A: Solve by using Cauchy-Riemann equations

Q: „Show that the complex variable function below is differentiable analytic only at origin point? f(z)…

A: We will show the required result.

Q: what is the area of the rotational surface formed by rotating the part of the function y= x^3/3…

A: We apply the above formula to solve this

Q: 2. Consider the function f(z) = where z is a complex variable defined as z = x + jy. nvestigate…

A: Given: The given function is fz=1z we want to check that whether given function is analytic or not…

Q: Determine a scalar equation for the plane that passes through the point (2, 0, -1) and is…

A:

Q: 8. The curl of gradient of a scalar function is (a) zero (c) unity (b) non-zero (d) depends on the…

A: the answer is option a.) zero the explanation is given in the below step

Q: Find a vector function that represents the curve of intersection of two surfaces: z = x² - y? and x²…

A: Idea  1) Solve the equation in term of only one variable (2) assume in term of parametric function…

Q: Express the functions ƒ(x, y) = (x2 + y2)5/2 and h(x, y) = x2 - y2 in polarcoordinates.

A:

Q: 1 Let f (z) %3D z - 7 Part (a) Integrate the function f (z)along the curve C in the complex plane…

A: Solution:-

Q: Current Attempt in Progress Find the scalar triple product u · (v x w). u-(-8,4,4), v- (5,1, - 4), w…

A: Given: u=-8,4,4, v=5,1,-4, w=-7,4,3 To find: u·(v×w)

Q: Find curl (3z i + 4x j+ 2y k). curl (3z i + 4x j+ 2y k) = ( Di + ( j +( )k

A:

Q: Cauchy Riemann equations are u = -v and u = – V х у у х ou =v and u = -v х у у х и 3Dу апаd и 3D — и…

A: Given that  Cauchy Riemann equation is

Q: he upward flux of

A: Introduction: Let F be a function and let the region is S, then the flux of the function is given…

Q: Calculate the frist order differential of the function f(x,y) = x^{4}*y^{2}+2*x-y^{7}+3

A: First order Partial derivatives

Q: Parametrize y = -x2 + 4 in terms of u and v %3D

A:

Q: Determine if the function satisfy the Cauchy-Riemann equations. 8. f(z) = z + Re(z)

A:

Q: Find the number of zeros of f(z) = 2z* – z + 5z – 1 in the annulus 1 < |z| < 2. %3D

A:

Q: a) Plot a direction field and some integral curves  for xy'-2y=-1 on the rectangular region {-1<or…

A: a) given differential equation  xy'-2y=-1 claim- plot a direction field and sole integral curves for…

Q: Let f(z)=y-2xy +i(-x+x² - y²)+z² where, z=x+iy is a complex variable defined in the whole complex…

A:

Q: Verify that the real-valued function u(x, y) = x^3 − 3xy^2 − 2y defined on the complex plane C is…

A:

Q: II. Use Cauchy – Reimann Equations to identify if it is differentiable or not, if yes then…

A: To answer the given question we shall use the following Proposition- Proposition: If f=u+jv , fx and…

Q: (4)Find the scalar function such that F = V ø y i+ where F=- *+y x+y

A: We can find scalar function ϕ such that F→=∇ϕ ;where ∇ =i^∂∂x+j^∂∂y+k^∂∂z

Q: Verify Cauchy-Riemann equation for the function f(z) = z^3

A: To find- Verify Cauchy-Riemann equation for the function fz = z3         Formula Used-…

Q: Find the streamlines of the flow associated with the given complex function. f(z) ==—=/ (x(t), y(t))…

A: To Find: Equation of Streamlines for the function f(z)=1z¯.

Q: Name a complex function that is defined on the entire plane and is continuous at all points except…

A: Continuous function

Q: (i) An electrostatic field in xy-plane is given by $(x, y) = 3x²y- y³. Find the stream function Y…

A:

Q: 1. Use Cauchy- Reimann Equations to identify if it is differentiable or not, if yes then…

A: We have to find out that the given equation is differentiable or not and if it differentiable then…

Q: se Cauchy-iemman equations to now that each of these functions is where cnalytic Rz= メ

A: Given: fz=xy+iy   -1 The objective is to show that the given function is nowhere analytic.

Q: Describe the loci zz−2z−2z+8 = 0 expressed in terms of conjugate coordinates z, z.

A: It is given thatzz¯-2z-2z¯+8=0Where,z¯ is the conjugate co-ordinate of z.We have describe the locus.

Q: Q3A) Using Cauchy Riemann equations show that: f(z) = 2z8z5 + 4z6 4z38z² + 2z is analytic in…

A:

Q: (a) Consider the equation e'ux+2ayuy +2e*uy-sin(y) u =0, where a is a real constant. Determine the…

A: We will use basic knowledge of PDEs to answer this question.

Q: Let w=iz2-4z+3i (where z is a complex variable z=x+iy) find delta(w), dw, and delta(w)-dw at the…

A: To calculate the difference and differential of the given function,

Q: f(2) = 2z2 – iz - be a complex valued function defined on a complex plane. Writing z = x + iy, find…

A:

Q: Find curl(7z i + 8x j+ 5y k). curl (7z i + &x j+ 5y k) = ( i )i + (i )j + ( )k

A:

Q: Answer the follwing questions. (a) Detemine whether fAz)=3z-z* is differentiable. (b) Let fz) be a…

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

Q: Y1 = 3 + 3/3i Y2 = -2 + 2/3i

A:

Q: Explain how the fundamental theorem of calculus relates integrals and derivatives. Formats T B T U…

A: Fundamental theorem of calculus relates integrals and derivatives.

Q: Answer the folwing questions. (a) Determine whether fAz)=3z²-zz* is differentiable. (b) Let fAz) be…

A: Determine whether f(z)=3z2-zz¯ is differentiable or not.A function f(z) is said to be differentiable…

Q: In differential geometry give me example of covariant tensor and contra variant tensor.

A: Concept:

Q: The imaginary part of the complex function f(z) = u + iv is, v(x, y) = 3x²y + 2x² – y³ – 2y² (i)…

A: For a function V(x,y) to be harmonic its Laplacian must be zero. i.e;

Q: derivatives of u, v and w with respect to x, y and z, and use them to compute Jacobian Obtain the…

A:

Q: Determine whether the given complex functions satisfy (have derivatives) the Cauchy-Riemann…

A:

Q: 4. f(z) = { |z|* z = 0 verify that the Cauchy-Riemann equations are satisfied at the origin z =(0,0)…

A: