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February 22nd, 2014, 08:16 PM   #1
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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 1-i.

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.
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February 23rd, 2014, 02:02 AM   #2
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Re: Find the image

Work with polar coordinates again.
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February 23rd, 2014, 08:59 AM   #3
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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.
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February 24th, 2014, 05:24 AM   #4
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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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