Mapping question I don't understand

1. Dec 5, 2013

Genericcoder

Hi I uploaded the question and its answer first of all I am not good at all in mapping I don't understand it that much like here we want the output of the function under that specific domain that's what we want to see.
I understand until PI < alpha < 5/2 * PI but I don't understand how did he get
f(D) = {|z| < 2 , -PI < Arg(z) < PI/2} I don't get that could someone please explain because I need to understand this.

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2. Dec 5, 2013

LCKurtz

If you take the range $\pi < \alpha <\frac 5 2 \pi$, you can subtract $2\pi$ from the $\pi$ and $\frac 5 2 \pi$ and it is the same region in the plane. So $-\pi < \alpha < \frac \pi 2$ describes the same region.

3. Dec 5, 2013

Genericcoder

Oh I see that makes alot of sense thank you !!!!

4. Dec 5, 2013

Genericcoder

could you please also like explain maybe more about this question about how did he arrive to this solution coz I am not sure that my understanding is correct or intuition is right..

5. Dec 5, 2013

Staff: Mentor

Which part don't you understand?

6. Dec 6, 2013

Genericcoder

So I was wondering how do we systematically solve stuff like this ? are we looking for how some function output under certain set of conditions ? like for example f(x) = x^2 and we restrict the domain to be something like
[0,2] and see what is the range of output we are trying to get ?? I don't really understand what's going on here I just know how to solve in some scenrios but I don't get are we actually doing ...

7. Dec 7, 2013

Genericcoder

Is there systematic way to do these kind of problems?