What do S1 and S2 look like on the complex plane under e^z?

[Polamaluisraw]

Complex Variables - Mappings under e^z

Homework Statement

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

Homework Equations

w=e^z
w=\rhoe^i\varphi
\rho=e^x, \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!

 

[SammyS]

Homework Statement

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

Homework Equations

w=e^z
w=\rhoe^i\varphi
\rho=e^x, \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.

 

[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

 

[SammyS]

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.)

 

[Polamaluisraw]

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