The complex number $z$ is given by $\frac{2}{1+ki} - \frac{i}{k-i}$. If it is given that $z$ lies on the line, $y = 2x$, find the value of the real scalar $k$. 

So far this is what I have come up with : (See attached photo)

I am stuck at this point. I think that, because the question asks for the value of the real scalar $k$, I should move forward with only the "$x$" part of the coordinate system, but I do not know what to do with it. 

Also, because it asks for the scalar value, I am wondering if I need to find the modulus of anything. 

Any help would be appreciated.