- #1

Raziel2701

- 128

- 0

**Show the pre-image of a vertical line Re(w)=c under f...**

## Homework Statement

a) Show that the pre-image of a vertical line Re(w)=c under f is a circle centered on the line Re(z) = -1 and tangent to the real axis Im(z) = 0.

b) How does such a circle intersect the circle |z| =1?

Here's f by the way: [tex]i\frac{1-z}{1+z}[/tex]

## The Attempt at a Solution

So I took f and set it equal to c:

[tex]i\frac{1-z}{1+z} =c[/tex]

Solving for z, I get that the Re(z)

[tex]Re(z) = \frac{-c^2 +1}{c^2 +1}[/tex]

So that was me not knowing what I'm doing and just messing with the given information. I then took the limit as z approaches infinity and I get -1, so I again, not knowing if I'm doing this right simply declared that Re(z) is now equal to -1 as I'm supposed to prove.

So am I doing this right?

For part b, the circles intersect twice at 90 degrees right?

Last edited: