Im given a question on an upper half plane such that you map a mobius transformation M(C(0,∞)) = C(0,4) and M(i) = 2 + i. Where C(a,b) denotes a circle with centre a and radius b.
How do I go about solving this. I used the equation $|w-0|^2$ = $4^2$ to get that M(C(0,∞)) = 4, likewise for $|z-0|^2 = ∞^2$, we get z=∞, thus we have a/c = 4.
M(i) = 2+i is simple enough, You get M(i)=$\frac{ai+b}{ci+d}$ = 2+i.
You can simplify this to $\frac{ai+b}{ci+d}$ - i = 2.
What I dont get is what to do from here. Any suggestions? I dont want a solution. Just a third equation so i can go about solving this. I cant think of any additional properties to use to get this third equation.