# Thread: Complex Analysis Question regarding mappings.

1. ## Complex Analysis Question regarding mappings.

I am studying for an exam and I missed this problem on a homework. Can someone help me with it so that I can understand it before the exam?

I tried an approx along the lines of Mx+b but I butchered the problem... TIA

Problem:

Find the linear transformation $w=f(z)$ that satisfies the following...

circle $|x|=1$ maps onto a circle $|w - 3 + 2i| = 5$ and $f(-i) = 3 + 3i$...

Any help would be appreciated...

2. ## Geometry

Think about it geometrically: you're mapping the unit circle to the circle with center 3-2i and radius 5, with the condition $f(-i)=3+3i$. What does $f(z)=Mz+b$ with complex M and Z mean geometrically? It means we scale by $|M|$, rotate by $\arg{M}$, and then translate by b. Does that help?

--Kevin C.