I'm trying to get the real roots of this expression:
$$\dfrac{1}{z-i}+\dfrac{2+i}{1+i} = \sqrt{2}$$
Where $i^2=-1$ and $z=x+iy$.
I tried to simplify that with Algebra, and then separate the real and imaginary parts in both sides of the expression to obtain an equation system, so I would solve it to obtain the roots for both $x$ and $y$. But all I get is a mess!
Any help would be appreciated, thank you! :)
P.S. It comes again from a Russian book, it says the answer is: there aren't real solutions. And with the procedure I said, I got real solutions!
P.P.S. I'd write down what I did, but I don't have the written steps anymore, sorry :(