# Complex analysis

physicsnewb7

## Homework Statement

write f(z)= (z+i)/(z^2+1) in the form w=u(x,y)+iv(x,y)

## The Attempt at a Solution

I tried using the conjugate and also expanding out algebraically but I can not seem to get the right answer. I know what the answer is, x/(x^2+(y-1)^2)+i(1-y)/(x^2+(y-1)^2) but I fail to see how to get there. am I doing something wrong?

physicsnewb7
all i want is a simple hint i don't want anyone to do the problem for me I just want a little help. just a little push in the right direction would be so helpful.

rizardon
Why don't you try and do the partial fraction. I think it should work.

physicsnewb7
Why don't you try and do the partial fraction. I think it should work.

So I do the partial fraction after i expand out? expanding (z+i)/(z^2+1) I get (x+yi+i)/(x^2+2xyi-y^2+1) how am I supposed to factor the denominator?

physicsnewb7
ohhhhh nevermind i finally got it you rewrite the denominator as (z+i)(z-i) then do the partial fraction. so simple! you were right rizardonthanks