February 22nd, 2014, 08:16 PM  #1 
Senior Member Joined: Jan 2014 Posts: 196 Thanks: 3  Find the image
Find the image of the ray under The answer I came up with on my own is a ray w/ emitting from 1i. The answer in the book has two things I do not understand. States that is not in the image and that is contained in the image. Thanks for any help on this. 
February 23rd, 2014, 02:02 AM  #2 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Find the image
Work with polar coordinates again.

February 23rd, 2014, 08:59 AM  #3 
Senior Member Joined: Jan 2014 Posts: 196 Thanks: 3  Re: Find the image
start with ; a) b) c)for r = 1 d) So far, am I approaching this correctly? Still not seeing how it is clear that is not in the image. 
February 24th, 2014, 05:24 AM  #4 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Find the image
Ok, your answer is correct and it describes the ray emitting from using function compositions. But why is not contained in the image this is simply because is not contained in . The definition of argument states that is undefined since polar coordinates are not useful to describe the point . If we say that the point describes the vector of radius then clearly the direction cannot be specified because a point has no direction. So is not mapped by the function so for otherwise . 

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