# Complex Variables - Mappings

Complex Variables - Mappings under e^z

## Homework Statement

Find the image of S1,S2 under ez.
S1 = {z=x+iy : 0 < y < $\pi$ }
S2 = {z=x+iy : x > 0, 0 < y < $\pi$ }

## Homework Equations

w=ez
w=$\rho$ei$\varphi$
$\rho$=ex, $\varphi$=y

## 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!

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SammyS
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Homework Helper
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## Homework Statement

Find the image of S1,S2 under ez.
S1 = {z=x+iy : 0 < y < $\pi$ }
S2 = {z=x+iy : x > 0, 0 < y < $\pi$ }

## Homework Equations

w=ez
w=$\rho$ei$\varphi$
$\rho$=ex, $\varphi$=y

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

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

SammyS
Staff Emeritus
Homework Helper
Gold Member
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
So, do you know what the sets S1 and S2 look like on the complex plane ?

(I tried to push you this way earlier.)

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

(I tried to push you this way earlier.)
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