
Complex Algebra
I'm a little rusty in complex algebra I was wondering how i would go about solving this equation for $\displaystyle w$
$\displaystyle \frac{w+i}{wi} = \frac{1+i}{1i}\left(\frac{z+1}{z1}\right)$
The correct answer being $\displaystyle w = \frac{iz}{i+z}$

Multiply both sides by (wi). Then move both terms to one side. Expand the term with (wi) and factorise w.

I'm not sure exactly what you're getting at, could you write some of the steps out?

The long way round?
$\displaystyle \dfrac{w+i}{wi} = \dfrac{1+i}{1i}\left(\dfrac{z+1}{z1}\right)$
$\displaystyle \dfrac{w+i}{wi} = \dfrac{z1+iz+i}{z1iz+i}$
$\displaystyle (w+i)(z1iz+i) = (z1+iz+i)(wi)$
$\displaystyle w(z1iz+i) + i(z1iz+i) = w(z1+iz+i)  i(z1+iz+i)$
$\displaystyle w(z1iz+i)  w(z1+iz+i) =  i(z1+iz+i)  i(z1iz+i)$
$\displaystyle w(z1iz+i +z+1izi) =  i(z1+iz+i + z1iz+i)$
$\displaystyle w(2z2iz) =  i(2+2i)$
$\displaystyle 2w(ziz) =  2i(1+i)$
$\displaystyle w(ziz) = i +1$
$\displaystyle w = \dfrac{i + 1}{ziz} = \dfrac{i}{z}$
Are you sure this is the correct question?

Thanks for taking the time to work it out, Unknown008!
Mathematica agrees with your answer.
Original poster, please check either your question or answer.

Sorry I was off by 1 on the RHS. it should be $\displaystyle \frac{1+i}{1i}\frac{z+1}{z1}$, but i have the general method now. thanks