The question:

For the mapping f(z) = \frac{z − i}{z + i}, ﬁnd the image of {z ∈C: Im(z) ≥ 0}

I'm confused as to how to attempt this. I tried setting f(z) = w, the rearranged to make z the subject. I then set w = a + ib and found the imaginary part. But it was just a big mess, and I'm fairly sure I have no idea what I'm doing. My text is quite brief on this topic.

Any assistance would be great.