Complex Variables - Mappings

  • #1
Complex Variables - Mappings under e^z

Homework Statement


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



Homework Equations


w=ez
w=[itex]\rho[/itex]ei[itex]\varphi[/itex]
[itex]\rho[/itex]=ex, [itex]\varphi[/itex]=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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Answers and Replies

  • #2
SammyS
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Homework Statement


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



Homework Equations


w=ez
w=[itex]\rho[/itex]ei[itex]\varphi[/itex]
[itex]\rho[/itex]=ex, [itex]\varphi[/itex]=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.
 
  • #3
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
SammyS
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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.)
 
  • #5
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
 

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