Complex Conjugate of f(z) = -(1-z)/(1+z)

[KleZMeR]

Homework Statement

Find U(x,y) and V(x,y) for f(z) = -(1-z)/(1+z)

Find Ux, Vy, Vx, Uy (partial derivatives)

Homework Equations

z = (x+iy)

The Attempt at a Solution

I found U(x,y) and V(x,y), and I used the quotient rule to find the partial derivatives Ux, Vy.

They should be equal given the C-R relation, but they are off by a factor of x in Vx. I am attaching my work, I have checked the algebra and am not seeing an error, maybe someone else has insight into my problem? Should I be using polar form to figure this out?

I've been killing myself on this one today, any help is appreciated.

 

[Ray Vickson]

Homework Statement

Find U(x,y) and V(x,y) for f(z) = -(1-z)/(1+z)

Find Ux, Vy, Vx, Uy (partial derivatives)

Homework Equations

z = (x+iy)

The Attempt at a Solution

I found U(x,y) and V(x,y), and I used the quotient rule to find the partial derivatives Ux, Vy.

They should be equal given the C-R relation, but they are off by a factor of x in Vx. I am attaching my work, I have checked the algebra and am not seeing an error, maybe someone else has insight into my problem? Should I be using polar form to figure this out?

I've been killing myself on this one today, any help is appreciated.

Glad to look at it if it is typed out; otherwise, not.

 

[KleZMeR]

Hi Ray, what is it that needs to be typed out? All my algebra? The solution?

 

[Ray Vickson]

Hi Ray, what is it that needs to be typed out? All my algebra? The solution?

The details of your work.

 

[KleZMeR]

Hi Ray, it was an algebra error. It seems most of my errors in my course homework are small algebraic errors that amount to big problems. I should work on my organization I guess. The concepts behind these topics I often understand, but when I make these errors it makes it hard to attack the real problem, getting bogged down with algebra. Thanks for responding, I'm sure I'll be posting again, and I will do my best to type out the details of my work.