# Homework Help: Complex Variables - Mappings

1. Feb 11, 2012

### Polamaluisraw

Complex Variables - Mappings under e^z

1. The problem statement, all variables and given/known data
Find the image of S1,S2 under ez.
S1 = {z=x+iy : 0 < y < $\pi$ }
S2 = {z=x+iy : x > 0, 0 < y < $\pi$ }

2. Relevant equations
w=ez
w=$\rho$ei$\varphi$
$\rho$=ex, $\varphi$=y

3. The attempt at a solution
Did not know how to get started. I don't know how to use the above equations to help me. Thank you very very much!

Last edited: Feb 11, 2012
2. Feb 11, 2012

### SammyS

Staff Emeritus
Re: Complex Variables - Mappings under e^z

You might start by identifying what the set, S1 and S2 are.

3. Feb 12, 2012

### Polamaluisraw

The answer the professor has is {ω= u + iv : v > 0}.

I really do not understand how to use the equations and arrive here. I HAVE to be missing something simple. I really appreciate any help that can push me into the right direction

4. Feb 12, 2012

### SammyS

Staff Emeritus
So, do you know what the sets S1 and S2 look like on the complex plane ?

(I tried to push you this way earlier.)

5. Feb 12, 2012

### Polamaluisraw

I do not know what it looks like in the complex plane. What can I do to help me visualize it?
I really appreciate the help