Question

Find the analytic function f(z)=u+iv given u-v=(x-y)
(x²+4xy+y^2)

Answer 1

Answer:

Analytic function F(z)= u + iv becomes

Step-by-step explanation:

Here, we have analytic function f(z)= u+iv

and given the real part value,

u = (x cos y - y sin y) ..........(1)

so, by the Cauchy Equations

Partially Differentiating Eq. (1) with respect to x, we get

.........(2)

Partially Differentiating Eq. (1) with respect to y, we get

........(3)

Eq. (3) equals to the  

or

..........(4)

Now,

integrated equation (4) with respect to x, we get

so, analytic function F(z)= u + iv becomes

Where, C is the airbitrary constant of integration.