$\displaystyle D^+=\left \{z:|z|<1,Im \left \{ z \right \}>0 \right \}$

so it represents the northen hemisphere of a circle with radius 1.

$\displaystyle f(z)=\frac{2z-i}{2-iz}$

i need to find what is the picture of $\displaystyle f(d^+)=? $

i tried to solve it like this:

my area is bounded by a line and a curve.

i want to see what each one transforms to

**curve points:**
f(1)=1

f(-1)=-1

f(i)=i/3

so it will look like this

http://i46.tinypic.com/3129rg4.gif **line points:**
f(1)=1

f(-1)=-1

f(0)=-i/2

so it looks like this

http://i49.tinypic.com/dnnh2u.jpg
and when i try and see where the inside goes :

f(i/2)=0

so the answer represents their intersection area

(i mistakenly marked only a part of the interssection marked it should be the whole intersection)

http://i49.tinypic.com/14bi2qr.gif
but my prof thinks otherwise

http://i48.tinypic.com/2jff52r.jpg
who is worng here? why?

so its in their intersections