Question

Asked Feb 24, 2019

1482 views

Verify that the Cauchy-Riemann equations are satisfied for the following functions. Where z is a complex variable z=x+iy

a) e^{z}^{^2}

b) cos(2z)

c) sinh(4z)

Step 1

To verify the Cauchy -Riemann equations for the given analytic functions f(z)

Step 2

Let f(z)=u(x,y)+iv(x,y) be an analytic function of z, with u and v the real and imaginary parts of f(z). Then u and v (as real functions ) satisfy the Cauchy -Riemann equations.

Step 3

(a) Cauchy Riemann for f(z)=...

Tagged in

Q: Use the definition of Laplace Transforms to show that:

A: Given:The laplace transformation,

Q: Abstract Algebra

A: To define the concept of a subfield of a field and prove the stated property regarding subfields of ...

Q: How many possible graphs can be created on 5 distinct vertices?

A: To calculate the total number of graphs with 5 vertices

Q: I need help for problem 1. Thanks!

A: Suppose there are two limits for f(x) as x tends to a named as l and m.Them, the uniqueness of limit...

Q: 1. Suppose that {an} and {b.) are bounded sequences. Show that lim sup an lim supbn. lim sup an +bn ...

A: As per norms, the first question is answered, To prove the property of lim sup under addition of seq...

Q: Prove that if p is a prime, then the square root of p is irrational.

A: Click to see the answer

Q: By finding suitable integrating factors, solve the following equations: (a) (1-x?)y' + 2xy (1-x2)3/2...

A: (a) Consider the given equation as equation (1) and obtain the integrating factor as follows.

Q: Abstract Algebra The problem and D3 is given in the below picture.

A: Click to see the answer

Q: Find the particular solutions to the given differential equations: y(3)+3y"-4y'-12y=0, y(0)=1, y'(0...

A: The initial value problem is,